Linear Functions Practice

Sample questions

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1. Sample 1difficulty 2/5

   The graph of $f(x) = 3x - 1$ is reflected across the $x$-axis. What is the new function?

   • A

     $g(x) = -3x - 1$

   • B

     $g(x) = 3x + 1$

   • C

     $g(x) = -(3x - 1)^2$

   • D

     $g(x) = -3x + 1$

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   Why

   Reflection across $x$-axis negates the output: $g(x) = -(3x-1) = -3x + 1$.

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2. Sample 2difficulty 2/5

   A phone plan: \25$monthly plus$$0.05$per minute. Cost for$m$ minutes is:

   • A

     $C = 25m + 0.05$

   • B

     $C = 0.05(m + 25)$

   • C

     $C = 25.05m$

   • D

     $C = 0.05m + 25$

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   Why

   Per-minute rate $0.05$ is slope; monthly fee $25$ is intercept.

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3. Sample 3difficulty 2/5

   For the linear function $f(x) = 4x - 9$, what is the average rate of change of $f$ from $x=2$ to $x=7$?

   • A

     9

   • B

     4

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   • C

     5

   • D

     3

   Why

   For any linear function, the average rate of change equals its slope: $4$.

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4. Sample 4difficulty 2/5

   A gym charges a $50 membership fee plus$20 per month. Which equation gives the total cost $C$ after $m$ months?

   • A

     $C = 20m + 50$

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   • B

     $C = 50m + 20$

   • C

     $C = 70m$

   • D

     $C = 50 + 20$

   Why

   Monthly rate $20$ is the slope; one-time fee $50$ is the y-intercept. $C = 20m + 50$.

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5. Sample 5difficulty 2/5

   A taxi fare is $F = 2.50d + 3$ where $d$ is miles. What is the meaning of $3$?

   • A

     Total fare

   • B

     Number of miles

   • C

     Cost per mile

   • D

     Initial flat fee

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   Why

   The y-intercept $3$ is the fare when $d = 0$ — the starting flat fee.

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