Introduction to Functions: Grade 8 Math Test – PDF Download

Question 1: Mapping diagram (2 points)

Does the mapping diagram show a function? Explain.

Question 2: Table of values (2 points)

A relation has inputs 1, 3, 3, 5 and outputs 4, 6, 8, 10 in that order. Is it a function? Explain.

Question 3: Evaluate (2 points)

For \(f(x)=-3x+5\), find \(f(-2)\) and \(f(4)\).

Question 4: Write an equation (2 points)

The inputs 1, 2, 3, 4 give outputs 5, 9, 13, 17. Write an equation for the function.

Question 5: Points on a line (3 points)

The graph shows four points of a function.

1. Is the function linear? Explain. (1 point)
2. Find the rate of change. (1 point)
3. Write an equation. (1 point)

Question 6: Linear or nonlinear? (3 points)

Classify each function as linear or nonlinear.

1. \(y=6x-2\) (1 point)
2. The area \(A=s^{2}\) of a square with side \(s\) (1 point)
3. \(x\): 1, 2, 3, 4 and \(y\): 2, 5, 10, 17 (1 point)

Question 7: Compare two functions (2 points)

Function A is \(y=5x+2\). Function B has the table: \(x\) = 0, 2, 4 and \(y\) = 1, 9, 17. Which function has the greater rate of change? Which has the greater initial value?

Question 8: Taxi fare (2 points)

A taxi charges $3 plus $2 per mile, so the fare is \(f(m)=2m+3\) dollars for \(m\) miles. Find the fare for 7 miles and the number of miles for a fare of $25.

Question 9: Area graph (2 points)

The graph shows the area of a square for sides 1, 2, 3 and 4. Is the function linear? Justify your answer using the graph or the values.

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