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Linear functions and graphs — ACT practice questions

Linear functions and graphs on the ACT Mathematics test covers constant-rate growth, slope and intercept in applied models, and average rate of change between two inputs. A student must write a function for a quantity that increases by the same amount each row or month, interpret each coefficient in context, and read slope from a graph or from two points. Questions are five-choice and usually ask which equation fits a pattern, which statement correctly reads a model, or what the average rate of change is. Common traps include swapping slope with intercept, treating the first row as zero, and confusing average rate of change with a function value.

  • Section: Mathematics 45 questions on the paper
  • 38 practice questions in the app

Sample questions

Question 1

A small theater has 18 seats in row 1, 24 seats in row 2, 30 seats in row 3, and 36 seats in row 4. If the number of seats continues to increase by 6 per row, which of the following equations gives the number S(r)S(r) of seats in row rr?

  1. AS(r)=6r+18S(r)=6r+18
  2. BS(r)=18r+6S(r)=18r+6
  3. CS(r)=18r−6S(r)=18r-6
  4. DS(r)=6r+12S(r)=6r+12
Show answer

Answer: D — S(r)=6r+12S(r)=6r+12

The increase of 6 seats per row gives a coefficient of 6. Since S(1) = 18, the constant must be 12, so S(r) = 6r + 12.

Question 2

The number of loaves a bakery sells monthly is modeled by L(m)=210+39mL(m)=210+39m, where mm is the number of months after the first month. Which of the following statements correctly interprets the numbers in this model?

  1. AThe bakery sells 210 loaves in the first month and then 39 more loaves each month.
  2. BThe bakery sells 39 loaves in the first month and then 210 more loaves each month.
  3. CThe bakery sells 39 loaves in the first month and then 210 fewer loaves each month.
  4. DThe bakery sells 210 loaves in the first month and then 39 fewer loaves each month.
Show answer

Answer: A — The bakery sells 210 loaves in the first month and then 39 more loaves each month.

Because m = 0 represents the first month, 210 is the starting value. The coefficient 39 means monthly sales increase by 39 loaves per month.

Question 3

For f(x)=2x2−3x+1f(x)=2x^2-3x+1, what is the average rate of change of ff from x=1x=1 to x=4x=4?

  1. A3
  2. B5
  3. C7
  4. D9
Show answer

Answer: C — 7

The function values are f(1)=0f(1)=0 and f(4)=21f(4)=21. The average rate of change is 21−04−1=7\dfrac{21-0}{4-1}=7.

Practice 38 Linear functions and graphs questions in the app

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