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!

This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like q(x) = x - 2x² at a specific value, we replace every x with that value and calculate: q(2) means substitute 2 for x, giving 2 - 2(2)². Starting with q(x) = x - 2x² and finding q(2), we substitute 2 for x everywhere: q(2) = 2 - 2(2)². Now we calculate step by step: first (2)² = 4, then 2(4) = 8, and finally 2 - 8 = -6. Choice A is correct because it properly substitutes 2 for x in the function and calculates accurately: 2 - 2(2)² = 2 - 2(4) = 2 - 8 = -6. Nice work if you got this! Choice D gives 6, which would result from making a sign error when subtracting, calculating 8 - 2 instead of 2 - 8. Remember, order matters in subtraction! 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 this problem, exponents come before multiplication, which comes before subtraction!

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!

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!

This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like $g(x) = -4(x - 1)$ at a specific value, we replace every x with that value and calculate: $g(0)$ means substitute 0 for x, giving $-4(0 - 1) = -4(-1) = 4$. Starting with $g(x) = -4(x - 1)$ and finding $g(0)$, we substitute 0 for x everywhere: $g(0) = -4(0 - 1)$. Now we calculate step by step: $0 - 1 = -1$, $-4(-1) = 4$. Choice B is correct because it properly substitutes 0 for x in the function and calculates accurately: $-4(-1) = 4$. Nice work if you got this! Choice A is a common slip-up: it makes a sign error, perhaps forgetting to multiply by -4 or mishandling the negative inside. Remember to follow the order of operations! 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!

This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like h(x) = x - 3 at a specific value, we replace every x with that value and calculate: h(0) means substitute 0 for x, giving 0 - 3 = -3. Starting with h(x) = x - 3 and finding h(0), we substitute 0 for x everywhere: h(0) = 0 - 3. Now we calculate step by step: -3. Choice B is correct because it properly substitutes 0 for x in the function and calculates accurately: 0 - 3 = -3. Nice work if you got this! Choice C is a common slip-up: it confuses what's being asked: it gives 0 instead of specifically finding h(0) by subtracting 3. 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. Think of a function as a machine: you put in an input (x = 0), the machine follows its rule (x - 3), and out comes an output (-3). The notation f(0) just means 'what does the machine output when I feed it 0?'

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!

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(-1), it means 'substitute -1 for every x in the function formula,' like filling in a blank everywhere you see x. When evaluating with a negative number like f(-1), we need to be extra careful with signs! Substituting -1 for x in f(x) = -2x + 6, we get -2(-1) + 6 = 2 + 6 = 8. Notice how the parentheses around -1 help keep track of the negative! Choice B is correct because it properly substitutes -1 for x in the function and calculates accurately: -2(-1) + 6 = 8. Nice work if you got this! Choice C is a common slip-up: it makes a sign error when working with the negative input -1. When you substitute a negative number, use parentheses to keep track: -2(-1) is +2, 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!

This question tests your understanding of function notation and how to evaluate functions by substituting input values. In real-world contexts, a function like H(t) = 3t + 10 gives us a formula to calculate one quantity (like height) from another (like weeks), and evaluating H(4) tells us the specific height after 4 weeks. In this problem, $H(4) = 3(4) + 10 = 12 + 10 = 22$ centimeters, which means the height after 4 weeks is 22 centimeters. The function helps us quickly answer 'what if' questions by just plugging in different input values! Choice A is correct because it properly substitutes 4 for t in the function and calculates accurately: $3(4) + 10 = 22$. Nice work if you got this! Choice C is a common slip-up: it makes an arithmetic error, calculating $3*4 + 10$ as $12 + 5$ or something similar. Double-checking your arithmetic is always a good idea! In word problems, always state what your answer means: don't just write 'H(4) = 22'—say 'H(4) = 22 centimeters, which is the height after 4 weeks.' This shows you understand what the math represents!

This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like s(x) = 5x - 2 at a specific value, we replace every x with that value and calculate: s(-4) means substitute -4 for x, giving 5(-4) - 2. When evaluating with a negative number like s(-4), we need to be extra careful with signs! Substituting -4 for x in s(x) = 5x - 2, we get s(-4) = 5(-4) - 2, which equals -20 - 2 = -22. Notice how multiplying a positive by a negative gives a negative result! Choice A is correct because it properly substitutes -4 for x in the function and calculates accurately: 5(-4) - 2 = -20 - 2 = -22. Nice work if you got this! Choice D (22) makes a sign error, possibly calculating 5(4) - 2 instead of 5(-4) - 2. Remember that multiplying a positive number by a negative number always gives a negative result! When substituting negative numbers, always use parentheses to protect yourself from sign errors: write s(-4) = 5(-4) - 2. The parentheses keep everything clear! 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.