Function Notation and Evaluation - Algebra 1

For the function $h(x)=-3(x+1)+5$ , evaluate $h(2)$ .
Answer: $-4$ This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like h(x) = -3(x + 1) + 5 at a specific value, we replace every x with that value and calculate: h(2) means substitute 2 for x, giving -3(2 + 1) + 5. Starting with h(x) = -3(x + 1) + 5 and finding h(2), we substitute 2 for x everywhere: h(2) = -3(2 + 1) + 5. Now we calculate step by step: first the parentheses (2 + 1) = 3, then -3(3) = -9, and finally -9 + 5 = -4. Choice A is correct because it properly substitutes 2 for x in the function and calculates accurately: -3(2 + 1) + 5 = -3(3) + 5 = -9 + 5 = -4. Nice work if you got this! Choice D (8) makes a sign error, possibly calculating 3(2 + 1) + 5 instead of -3(2 + 1) + 5. Remember to carefully follow the signs given in the function, especially negative coefficients! Think of a function as a machine: you put in an input (x = 2), the machine follows its rule (-3(x + 1) + 5), and out comes an output (-3(3) + 5 = -4). The notation h(2) just means 'what does the machine output when I feed it 2?' Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations.
If $g(x)=x^2+3x-4$ , what is $g(-2)$ ?
Answer: $-6$ This question tests your understanding of function notation and how to evaluate functions by substituting input values. Function notation g(x) tells us the rule for calculating outputs from inputs: when you see g(-2), it means 'substitute -2 for every x in the function formula,' like filling in a blank everywhere you see x. When evaluating with a negative number like g(-2), we need to be extra careful with signs! Substituting -2 for x in g(x) = x² + 3x - 4, we get g(-2) = (-2)² + 3(-2) - 4, which equals 4 + (-6) - 4 = 4 - 6 - 4 = -6. Notice how the parentheses around -2 help keep track of the negative! Choice A is correct because it properly substitutes -2 for x in the function and calculates accurately: (-2)² = 4, 3(-2) = -6, so 4 + (-6) - 4 = -6. Nice work if you got this! Choice B gives -14, which results from forgetting that (-2)² = 4 (positive!) and incorrectly calculating it as -4. Remember, a negative number squared is always positive! When substituting negative numbers, always use parentheses to protect yourself from sign errors: write g(-2) = (-2)² + 3(-2) - 4, not g(-2) = -2² + 3(-2) - 4. The parentheses keep everything clear!
For $h(x) = -x^2 + 4$ , what is $h(2)$ ?
Answer: $0$ This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like h(x) = -x² + 4 at a specific value, we replace every x with that value and calculate: h(2) means substitute 2 for x, giving -(2)² + 4 = -4 + 4 = 0. Starting with h(x) = -x² + 4 and finding h(2), we substitute 2 for x everywhere: h(2) = -(2)² + 4. Now we calculate step by step: (2)² = 4, -4 + 4 = 0. Choice A is correct because it properly substitutes 2 for x in the function and calculates accurately: -4 + 4 = 0. Nice work if you got this! Choice C is a common slip-up: it makes a sign error by forgetting the negative sign in front of x², calculating (2)² + 4 = 8 instead. Remember to apply the negative to the squared term! Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations. For example: f(x) = 3x - 2, find f(4) → f(4) = 3(4) - 2 = 12 - 2 = 10. Easy!
Given $f(x) = 2 - 5x$ , what is $f(0)$ ?
Answer: $2$ This question tests your understanding of function notation and how to evaluate functions by substituting input values. Function notation f(x) tells us the rule for calculating outputs from inputs: when you see f(0), it means 'substitute 0 for every x in the function formula,' like filling in a blank everywhere you see x. Starting with f(x) = 2 - 5x and finding f(0), we substitute 0 for x everywhere: f(0) = 2 - 5(0). Now we calculate step by step: 5(0) = 0, so 2 - 0 = 2. Choice B is correct because it properly substitutes 0 for x in the function and calculates accurately: 2 - 0 = 2. Nice work if you got this! Choice A is a common slip-up: it substitutes correctly but then makes an arithmetic error, calculating 2 - 5(0) as -5 instead of 2. Double-checking your arithmetic is always a good idea! Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations. For example: f(x) = 3x - 2, find f(4) → f(4) = 3(4) - 2 = 12 - 2 = 10. Easy!
If $f(x)=4-2x$ , what does $f(5)$ equal?
Answer: $-6$ This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like f(x) = 2x + 5 at a specific value, we replace every x with that value and calculate: f(3) means substitute 3 for x, giving 2(3) + 5 = 6 + 5 = 11. Starting with f(x) = 4 - 2x and finding f(5), we substitute 5 for x everywhere: f(5) = 4 - 2(5). Now we calculate step by step: 4 - 10 = -6. Choice B is correct because it properly substitutes 5 for x in the function and calculates accurately: 4 - 2(5) = -6. Nice work if you got this! Choice A is a common slip-up: it makes an order of operations mistake or sign error, perhaps calculating 4 - 2 + 5 or 4 + 2(5) = 14. Remember, subtraction comes after multiplying! Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations. To check your work, ask yourself: 'Did I replace every single x with my input value?' and 'Did I follow PEMDAS for my calculation?' These two checks catch most mistakes!
Given the function $f(x)=2x-3$ , what is $f(4)$ ?
Answer: $5$ This question tests your understanding of function notation and how to evaluate functions by substituting input values. Function notation f(x) tells us the rule for calculating outputs from inputs: when you see f(4), it means 'substitute 4 for every x in the function formula,' like filling in a blank everywhere you see x. Starting with f(x) = 2x - 3 and finding f(4), we substitute 4 for x everywhere: f(4) = 2(4) - 3. Now we calculate step by step: 2(4) - 3 = 8 - 3 = 5. Choice A is correct because it properly substitutes 4 for x in the function and calculates accurately: 2(4) - 3 = 5. Nice work if you got this! Choice B has the right idea but makes an arithmetic error, calculating 2(4) + 3 = 11 instead of 2(4) - 3 = 5. Double-checking your arithmetic is always a good idea! Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations.
If $m(x)=2x^2-3x+1$ , evaluate $m(-1)$ .
Answer: $6$ This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like m(x) = 2x² - 3x + 1 at a specific value, we replace every x with that value and calculate: m(-1) means substitute -1 for x, giving 2(-1)² - 3(-1) + 1. When evaluating with a negative number like m(-1), we need to be extra careful with signs! Substituting -1 for x in m(x) = 2x² - 3x + 1, we get m(-1) = 2(-1)² - 3(-1) + 1, which equals 2(1) + 3 + 1 = 2 + 3 + 1 = 6. Notice how the parentheses around -1 help keep track of the negative! Choice D is correct because it properly substitutes -1 for x in the function and calculates accurately: 2(-1)² - 3(-1) + 1 = 2(1) + 3 + 1 = 6. Nice work if you got this! Choice A (0) might result from sign errors, possibly calculating 2(-1) - 3(-1) + 1 without squaring the first term. Remember to follow the function formula exactly as written! When substituting negative numbers, always use parentheses to protect yourself from sign errors: write m(-1) = 2(-1)² - 3(-1) + 1. The parentheses keep everything clear! Remember that (-1)² = 1 and -3(-1) = +3, so negative inputs can lead to positive terms!
Given $p(x)=4(x-2)$ , what is the value of $p(3)$ ?
Answer: $4$ This question tests your understanding of function notation and how to evaluate functions by substituting input values. Function notation p(x) tells us the rule for calculating outputs from inputs: when you see p(3), it means 'substitute 3 for every x in the function formula,' like filling in a blank everywhere you see x. Starting with p(x) = 4(x - 2) and finding p(3), we substitute 3 for x everywhere: p(3) = 4(3 - 2). Now we calculate step by step: first the parentheses 3 - 2 = 1, then multiply by 4 to get 4(1) = 4. Choice A is correct because it properly substitutes 3 for x in the function and calculates accurately: 4(3 - 2) = 4(1) = 4. Nice work if you got this! Choice B gives 12, which is a common slip-up: it multiplies 4 times 3 first to get 12, then subtracts 2 to get 10, or distributes incorrectly. Remember to handle what's inside parentheses first! Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations. Always do operations inside parentheses before multiplying!
Given the function $f(x)=2x-7$ , what is $f(4)$ ?
Answer: $1$ This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like f(x) = 2x - 7 at a specific value, we replace every x with that value and calculate: f(4) means substitute 4 for x, giving 2(4) - 7 = 8 - 7 = 1. Starting with f(x) = 2x - 7 and finding f(4), we substitute 4 for x everywhere: f(4) = 2(4) - 7. Now we calculate step by step: 2(4) = 8, then 8 - 7 = 1. Choice B is correct because it properly substitutes 4 for x in the function and calculates accurately: 2(4) - 7 = 8 - 7 = 1. Nice work if you got this! Choice A (-15) makes a sign error, possibly calculating -2(4) - 7 instead of 2(4) - 7. Remember to carefully follow the signs given in the function! Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations. For example: f(x) = 3x - 2, find f(4) → f(4) = 3(4) - 2 = 12 - 2 = 10. Easy!
A movie theater charges $9 per ticket plus a one-time online fee of $2. The total cost is $T(x) = 9x + 2$ . What is $T(3)$ ?
Answer: $29$ This question tests your understanding of function notation and how to evaluate functions by substituting input values in a real-world context. In real-world contexts, a function like T(x) = 9x + 2 gives us a formula to calculate one quantity (like cost) from another (like number of tickets), and evaluating T(3) tells us the specific cost when 3 tickets are involved. In this problem, T(3) = 9(3) + 2 = 27 + 2 = 29 dollars, which means the total cost for 3 tickets is 29 dollars. The function helps us quickly answer 'what if' questions by just plugging in different input values! Choice A is correct because it properly substitutes 3 for x in the function and calculates accurately: 27 + 2 = 29. Nice work if you got this! Choice B is a common slip-up: it substitutes correctly but then makes an arithmetic error, calculating 9(3) as 27 but forgetting to add the 2, or miscounting. Double-checking your arithmetic is always a good idea! In word problems, always state what your answer means: don't just write 'T(3) = 29'—say 'T(3) = 29 dollars, which is the total cost for 3 tickets.' This shows you understand what the math represents!
A streaming service charges $12 per month plus a one-time sign-up fee of $5. The total cost after $m$ months is $S(m) = 12m + 5$ . What is $S(2)$ ?
Answer: $29$ This question tests your understanding of function notation and how to evaluate functions by substituting input values in a real-world context. In real-world contexts, a function like $S(m) = 12m + 5$ gives us a formula to calculate one quantity (like cost) from another (like number of months), and evaluating $S(2)$ tells us the specific cost after 2 months. In this problem, $S(2) = 12(2) + 5 = 24 + 5 = 29$ dollars, which means the total cost after 2 months is 29 dollars. The function helps us quickly answer 'what if' questions by just plugging in different input values! Choice A is correct because it properly substitutes 2 for m in the function and calculates accurately: $24 + 5 = 29$ . Nice work if you got this! Choice B is a common slip-up: it substitutes correctly but then makes an arithmetic error, calculating $12(2)$ as 24 but forgetting to add the 5. Double-checking your arithmetic is always a good idea! In word problems, always state what your answer means: don't just write ' $S(2) = 29$ '—say ' $S(2) = 29$ dollars, which is the total cost after 2 months.' This shows you understand what the math represents!
For $k(x)=x^2-1$ , find both $k(3)$ and $k(-3)$ .
Answer: $k(3)=8$ and $k(-3)=8$ This question tests your understanding of function notation and how to evaluate functions by substituting input values. Function notation f(x) tells us the rule for calculating outputs from inputs: when you see f(3), it means 'substitute 3 for every x in the function formula,' like filling in a blank everywhere you see x. When evaluating with a negative number like k(-3), we need to be extra careful with signs! Substituting -3 for x in k(x) = x² - 1, we get (-3)² - 1 = 9 - 1 = 8, and for k(3) = (3)² - 1 = 9 - 1 = 8. Notice how the parentheses around -3 help keep track of the negative! Choice A is correct because it properly substitutes both 3 and -3 for x and calculates accurately: both give 8. Nice work if you got this! Choice B is a common slip-up: it makes a sign error when working with the negative input -3, perhaps thinking (-3)² is -9 instead of 9. When you substitute a negative number, use parentheses to keep track: (-3)² is positive, but forgetting parentheses can lead to the wrong sign. When substituting negative numbers, always use parentheses to protect yourself from sign errors: write k(-3) = (-3)² - 1, not -3² - 1. The parentheses keep everything clear!
Given $p(x)=4(x-1)$ , what does $p(5)$ equal?
Answer: $16$ This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like p(x) = 4(x - 1) at a specific value, we replace every x with that value and calculate: p(5) means substitute 5 for x, giving 4(5 - 1). Starting with p(x) = 4(x - 1) and finding p(5), we substitute 5 for x everywhere: p(5) = 4(5 - 1). Now we calculate step by step: 4(5 - 1) = 4(4) = 16. Choice B is correct because it properly substitutes 5 for x in the function and calculates accurately: 4(5 - 1) = 16. Nice work if you got this! Choice A treats p(5) as multiplication (4 times 5 plus something), but function notation uses parentheses to show the input, not to multiply. Think of p as a 'machine' that processes inputs, not as a number to multiply with. Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations. For example: p(x) = 4(x - 1), find p(5) → p(5) = 4(5 - 1) = 4(4) = 16. Easy!
If $f(x) = 10 - 3x$ , what is the value of $f(4)$ ?
Answer: $-2$ This question tests your understanding of function notation and how to evaluate functions by substituting input values. Function notation f(x) tells us the rule for calculating outputs from inputs: when you see f(4), it means 'substitute 4 for every x in the function formula,' like filling in a blank everywhere you see x. Starting with f(x) = 10 - 3x and finding f(4), we substitute 4 for x everywhere: f(4) = 10 - 3(4). Now we calculate step by step: 3(4) = 12, 10 - 12 = -2. Choice B is correct because it properly substitutes 4 for x in the function and calculates accurately: 10 - 12 = -2. Nice work if you got this! Choice D is a common slip-up: it has the right idea but makes an order of operations mistake, perhaps calculating 10 - 3 as 7 then multiplying by 4 to get 28, but we should multiply first following PEMDAS. Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations. For example: f(x) = 3x - 2, find f(4) → f(4) = 3(4) - 2 = 12 - 2 = 10. Easy!
For the function $h(x)=-3x+7$ , evaluate $h(-2)$ .
Answer: $13$ This question tests your understanding of function notation and how to evaluate functions by substituting input values. Function notation h(x) tells us the rule for calculating outputs from inputs: when you see h(-2), it means 'substitute -2 for every x in the function formula,' like filling in a blank everywhere you see x. When evaluating with a negative number like h(-2), we need to be extra careful with signs! Substituting -2 for x in h(x) = -3x + 7, we get h(-2) = -3(-2) + 7, which equals 6 + 7 = 13. Notice how the parentheses around -2 help keep track of the negative! Choice B is correct because it properly substitutes -2 for x in the function and calculates accurately: -3(-2) + 7 = 13. Nice work if you got this! Choice A makes a sign error when working with the negative input -2, calculating -3(-2) as -6 instead of +6. When you substitute a negative number, remember that a negative times a negative is positive! When substituting negative numbers, always use parentheses to protect yourself from sign errors: write h(-2) = -3(-2) + 7, not h(-2) = -3-2 + 7. The parentheses keep everything clear!
For the function $f(x) = 3x - 7$ , evaluate $f(-2)$ .
Answer: $-13$ This question tests your understanding of function notation and how to evaluate functions by substituting input values. Function notation f(x) tells us the rule for calculating outputs from inputs: when you see f(-2), it means 'substitute -2 for every x in the function formula,' like filling in a blank everywhere you see x. When evaluating with a negative number like f(-2), we need to be extra careful with signs! Substituting -2 for x in f(x) = 3x - 7, we get 3(-2) - 7, which equals -6 - 7 = -13. Notice how the parentheses around -2 help keep track of the negative! Choice C is correct because it properly substitutes -2 for x in the function and calculates accurately: 3(-2) - 7 = -13. Nice work if you got this! Choice B is a common slip-up: it makes a sign error when working with the negative input -2. When you substitute a negative number, use parentheses to keep track: 3(-2) is -6, but forgetting parentheses can lead to the wrong sign. When substituting negative numbers, always use parentheses to protect yourself from sign errors: write f(-3) = 2(-3)² + 1, not f(-3) = 2-3² + 1. The parentheses keep everything clear!
Given $f(x) = -3x - 2$ , evaluate $f(3)$ .
Answer: $-11$ This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like $f(x) = -3x - 2$ at a specific value, we replace every x with that value and calculate: $f(3)$ means substitute 3 for x, giving $-3(3) - 2 = -9 - 2 = -11$ . Starting with $f(x) = -3x - 2$ and finding $f(3)$ , we substitute 3 for x everywhere: $f(3) = -3(3) - 2$ . Now we calculate step by step: $-9 - 2 = -11$ . Choice A is correct because it properly substitutes 3 for x in the function and calculates accurately: $-9 - 2 = -11$ . Nice work if you got this! Choice B is a common slip-up: it makes a sign error, calculating -3*3 as +9 or forgetting the negative. Remember to apply the negative to the whole term! Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations. To check your work, ask yourself: 'Did I replace every single x with my input value?' and 'Did I follow PEMDAS for my calculation?' These two checks catch most mistakes!
Given $g(x)=x^2-4x+1$ , what is $g(3)$ ?
Answer: $-2$ This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like f(x) = 2x + 5 at a specific value, we replace every x with that value and calculate: f(3) means substitute 3 for x, giving 2(3) + 5 = 6 + 5 = 11. Starting with g(x) = x² - 4x + 1 and finding g(3), we substitute 3 for x everywhere: g(3) = (3)² - 4(3) + 1. Now we calculate step by step: 9 - 12 + 1 = -2. Choice A is correct because it properly substitutes 3 for x in the function and calculates accurately: 9 - 12 + 1 = -2. Nice work if you got this! Choice D is a common slip-up: it makes a sign error, perhaps calculating 9 - 12 + 1 as -3 + 1 = -2 but then flipping the sign to positive. Double-checking your arithmetic is always a good idea! Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations. For example: f(x) = 3x - 2, find f(4) → f(4) = 3(4) - 2 = 12 - 2 = 10. Easy!
If $s(x)=x^2+2$ , what is $s(-4)$ ?
Answer: $18$ This question tests your understanding of function notation and how to evaluate functions by substituting input values. Function notation s(x) tells us the rule for calculating outputs from inputs: when you see s(-4), it means 'substitute -4 for every x in the function formula,' like filling in a blank everywhere you see x. When evaluating with a negative number like s(-4), we need to be extra careful with signs! Substituting -4 for x in s(x) = x² + 2, we get s(-4) = (-4)² + 2, which equals 16 + 2 = 18. Notice how the parentheses around -4 help us remember that (-4)² = 16 (positive!). Choice B is correct because it properly substitutes -4 for x in the function and calculates accurately: (-4)² = 16, then 16 + 2 = 18. Nice work if you got this! Choice C gives -18, which would result from incorrectly thinking (-4)² = -16 instead of +16. Remember, a negative number squared is always positive! When substituting negative numbers, always use parentheses to protect yourself from sign errors: write s(-4) = (-4)² + 2, not s(-4) = -4² + 2. The parentheses make all the difference!
For $h(x) = (x + 5)^2$ , what is $h(-5)$ ?
Answer: $0$ This question tests your understanding of function notation and how to evaluate functions by substituting input values. Function notation h(x) tells us the rule for calculating outputs from inputs: when you see h(-5), it means 'substitute -5 for every x in the function formula,' like filling in a blank everywhere you see x. When evaluating with a negative number like h(-5), we need to be extra careful with signs! Substituting -5 for x in h(x) = (x + 5)², we get (-5 + 5)², which equals (0)² = 0. Notice how the parentheses around -5 help keep track of the negative! Choice A is correct because it properly substitutes -5 for x in the function and calculates accurately: (0)² = 0. Nice work if you got this! Choice C is a common slip-up: it calculates without the parentheses, like -5 + 5² = -5 + 25 = 20, but that's not the right order. When substituting negative numbers, always use parentheses to protect yourself from sign errors: write f(-3) = 2(-3)² + 1, not f(-3) = 2-3² + 1. The parentheses keep everything clear!

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