Function Definitions & Notation - ACT Math

Given $f(x)=\dfrac{2x-1}{x+3}$ , what is $f(1)$ ? Substitute $x=1$ : $f(1)=\dfrac{2(1)-1}{1+3}$ .
Answer: $\dfrac{1}{4}$ We need to find f(1) when f(x) = (2x - 1)/(x + 3). Substituting x = 1 into the function: f(1) = (2(1) - 1)/(1 + 3) = (2 - 1)/(1 + 3) = 1/4. The answer is 1/4. Be careful to substitute x = 1 in both the numerator and denominator.
Which of the following represents $f(x+4)$ if $f(x) = 2x^2 - x$ ?
Answer: $2(x+4)^2 - (x+4)$ We need to find f(x + 4) when f(x) = 2x² - x. To find f(x + 4), we replace every x in the original function with (x + 4): f(x + 4) = 2(x + 4)² - (x + 4). This expression shows the direct substitution before any expansion. Choice D correctly represents this substitution form. Note that f(x + 4) means substituting (x + 4) for every x, not adding 4 to the result.
A function is defined by $f(x)=5x+2$ . What is the value of $f(3)-f(1)$ ? Use substitution: $f(3)=5(3)+2$ and $f(1)=5(1)+2$ .
Answer: $10$ We need to find f(3) - f(1) when f(x) = 5x + 2. First, f(3) = 5(3) + 2 = 15 + 2 = 17. Next, f(1) = 5(1) + 2 = 5 + 2 = 7. Therefore, f(3) - f(1) = 17 - 7 = 10. The answer is 10.
If $f(x) = 2x^2 - 3x + 4$ , what is $f(0)$ ?
Answer: 4 We need to find f(0) when f(x) = 2x² - 3x + 4. To evaluate f(0), we substitute x = 0 everywhere it appears: f(0) = 2(0)² - 3(0) + 4 = 0 - 0 + 4 = 4. The answer is 4.
A function is defined by $f(x)=4x^2-x$ . What is $f(2)$ ?
Answer: $14$ We need to find f(2) where f(x) = 4x² - x. Substituting x = 2 into the function: f(2) = 4(2²) - 2 = 4(4) - 2 = 16 - 2 = 14. Following the order of operations, we calculate the exponent first, then multiplication, then subtraction.
If $f(x) = 8x - 3$ , what is $f(4)$ ?
Answer: 29 We need to find $f(4)$ when $f(x) = 8x - 3$ . To evaluate $f(4)$ , we substitute x = 4 into the function: $f(4) = 8(4) - 3$ . Following order of operations, we calculate $8(4) = 32$ , then $32 - 3 = 29$ . Therefore, $f(4) = 29$ .
If $f(x) = 2x^2 - 5x + 4$ , what is $f(3)$ ?
Answer: 7 We need to find f(3) when f(x) = 2x² - 5x + 4. To evaluate f(3), we substitute x = 3 into the function: f(3) = 2(3)² - 5(3) + 4. Following order of operations, we calculate 2(3)² = 2(9) = 18, then 5(3) = 15, so f(3) = 18 - 15 + 4 = 7. Therefore, f(3) = 7.
What is $f(3)$ if $f(x) = 2x + 5$ ?
Answer: 11 We need to find $f(3)$ when $f(x) = 2x + 5$ . To evaluate $f(3)$ , we substitute $x = 3$ into the function: $f(3) = 2(3) + 5 = 6 + 5 = 11$ . The answer is 11.
Given $f(x)=5x+2$ , which statement is true?
Answer: $f(x+1)=f(x)+5$ We need to determine which statement is true when f(x) = 5x + 2. Let's find f(x+1): f(x+1) = 5(x+1) + 2 = 5x + 5 + 2 = 5x + 7. Also, f(x) + 5 = (5x + 2) + 5 = 5x + 7. Therefore, f(x+1) = f(x) + 5 is true.
If $f(x) = 7 - x$ , what is $f(3)$ ?
Answer: 4 We need to find f(3) when f(x) = 7 - x. To evaluate f(3), we substitute x = 3 into the function: f(3) = 7 - 3. Following order of operations, we calculate 7 - 3 = 4. Therefore, f(3) = 4.
A function is defined by $f(x)=\dfrac{x+2}{x-3}$ . What is $f(1)$ ? Show the substitution: $f(x)=\dfrac{x+2}{x-3}$ , so $f(1)=\dfrac{1+2}{1-3}$ .
Answer: $-\dfrac{3}{2}$ We need to find f(1) when f(x) = (x+2)/(x-3). Substituting 1 for x: f(1) = (1+2)/(1-3) = 3/(-2) = -3/2. The answer is -3/2. Remember that when the denominator is negative, the entire fraction becomes negative.
A function is defined by $f(x)=x^2-1$ . What is the value of $f(\,x+1\,)$ ?
Answer: $x^2+2x$ We need to find f(x+1) where f(x) = x² - 1. This means replacing every x with (x+1): f(x+1) = (x+1)² - 1. Expanding the squared term: (x+1)² = x² + 2x + 1, so f(x+1) = x² + 2x + 1 - 1 = x² + 2x. The -1 and +1 cancel out.
A function is defined by $f(x)=x^2+2x-5$ . What is $f(-1)$ ?
Answer: $-6$ We need to find f(-1) where f(x) = x² + 2x - 5. Substituting x = -1 with parentheses: f(-1) = (-1)² + 2(-1) - 5 = 1 - 2 - 5 = -6. Remember that (-1)² = 1, not -1, since we're squaring the entire negative number.
What is the value of $f(-1)$ if $f(x) = x^2 + 2x + 1$ ?
Answer: 0 We need to find f(-1) when f(x) = x² + 2x + 1. To evaluate f(-1), we substitute x = -1 everywhere it appears: f(-1) = (-1)² + 2(-1) + 1 = 1 - 2 + 1 = 0. The calculation gives us 0.
If $f(x)=\dfrac{2x-1}{3}$ , what is $f(x-4)$ ? Substitute $(x-4)$ for every $x$ : $f(x-4)=\dfrac{2(x-4)-1}{3}$ .
Answer: $\dfrac{2x-9}{3}$ We need to find f(x-4) when f(x) = (2x-1)/3. Substituting (x-4) for every x: f(x-4) = (2(x-4)-1)/3 = (2x-8-1)/3 = (2x-9)/3. The answer is (2x-9)/3. Don't confuse f(x-4) with f(x) - 4; we must substitute (x-4) into the function.
If $f(x) = 3x + 8$ , what is $f(-2)$ ?
Answer: 2 We need to find f(-2) when f(x) = 3x + 8. To evaluate f(-2), we substitute x = -2 into the function: f(-2) = 3(-2) + 8. Following order of operations, we calculate 3(-2) = -6, then -6 + 8 = 2. Therefore, f(-2) = 2.
If $f(x)=\dfrac{x-6}{2}$ , what is the value of $f(0)$ ? Substitute $x=0$ : $f(0)=\dfrac{0-6}{2}$ .
Answer: $-3$ We need to find f(0) when f(x) = (x - 6)/2. Substituting x = 0 into the function: f(0) = (0 - 6)/2 = -6/2 = -3. The answer is -3. Be careful with the negative sign: 0 - 6 = -6, and -6 divided by 2 is -3.
A function is defined by $f(x)=\dfrac{x+6}{3}$ . What is $f(-3)$ ?
Answer: $1$ We need to find f(-3) where f(x) = (x+6)/3. Substituting x = -3: f(-3) = (-3+6)/3 = 3/3 = 1. We first perform the addition in the numerator, then divide by 3.
What is $f(-3)$ if $f(x) = 5x^2 - 4x + 1$ ?
Answer: 58 We need to find f(-3) when $f(x) = 5x^2 - 4x + 1$ . To evaluate f(-3), we substitute x = -3 into the function: $f(-3) = 5(-3)^2 - 4(-3) + 1$ . Following order of operations, we calculate $5(-3)^2 = 5(9) = 45$ , then $4(-3) = -12$ , so $f(-3) = 45 - (-12) + 1 = 45 + 12 + 1 = 58$ . Therefore, $f(-3) = 58$ .
If $f(x) = 2x^2 - x + 1$ , what is $f(0)$ ?
Answer: 1 We need to find f(0) when $f(x) = 2x^2 - x + 1$ . To evaluate f(0), we substitute x = 0 into the function: $f(0) = 2(0)^2 - 0 + 1$ . Following order of operations, we calculate $2(0)^2 = 2(0) = 0$ , then $0 - 0 + 1 = 1$ . Therefore, f(0) = 1.

Start this quiz