Functions and Graphs Practice Problems

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Functions and Graphs Practice Problems

Directions: Use scratch paper to solve the following problem. You can check your answer at the end of this section.

Practice

1. Using the function, f(x) = 5x – 1, find f(3).
2. The following shows the relationship between two variables: x and y. Write a description of the relationship shown.

   x	y
   0	0
   1	—
   2	4
   3	—
   4	16

3. If the function f is defined by f(x) = 9x + 3, which of the following is equal to f(4b)?
   1. 36b + 12b
   2. 36b + 12
   3. 36b + 3
   4. 
   5. + 3
4. Graph the equation y = x + 2.
5. Graph the inequality 3x + 2y ≤ 4. (Hint: Remember that the first step is to change the equation to y = form.)

Solutions

1. f(3) = 5(3) – 1 = 15 – 1 = 14. So, f(3) = 14.
2. The y-value is the x-value squared.
3. If f(x) = 9x + 3, then, for f(4b), 4b simply replaces x in 9x + 3. Therefore, f(4b) = 9(4b) + 3 = 36b + 3.
4. Start with the y-intercept, which is a positive 2. From there, go down 2, because the slope is negative, and to the right 3. Draw a line to connect the origin and the endpoint.



5. Subtract 3x from both sides of the inequality. 3x – 3x + 2y ≤ 4 – 3x

Simplify. 2y ≤ 4 – 3x

Use the commutative property. 2y ≤ –3x + 4

Divide both sides of the inequality by 2. ≤ +

Simplify both sides of the inequality. y ≤ + 2

The y-intercept of the inequality is 2 and the slope is . Start with the y-intercept, which is 2. From that point, go down 3 because the slope is negative and to the right 2. Then connect the starting point and the ending point. Will the boundary line be dotted or solid? It will be solid because the inequality symbol is ≤. Will you shade above or below the boundary line? You will shade below the boundary line because the inequality symbol is ≤.