Question 1

Given the function $$g(x) = 2x + 5$$, what is the value of $$g(a + 1)$$?

Accepted Answer

$$2a + 7$$

Question 2

If $$f(x) = 7x + 9$$, what is $$f(2x - 1)$$?

Accepted Answer

$$14x + 2$$

Question 3

If $$h(x) = x^2$ - 5$$, find $$h(x - 3).$$

Accepted Answer

$$x^2 - 6x + 4$

Question 4

Given $$f(x) = 2x^2$ - 2x + 7$$, what is $$f(x - 1)$$?

Accepted Answer

$$2x^2 - 6x + 11$

Question 5

If $$f(x) = -3x^2$ - 8x + 3$$, what is $$f(2x)$$?

Accepted Answer

$$-12x^2 - 16x + 3$

Question 6

Given $$f(x) = -3x^2$ - 8x + 5$$, what is $$f(x - 4)$$?

Accepted Answer

Question 7

A company models its profit $$P(x) in $$thousands of dollars by $$P(x) = 5x^2$ - 20x + 100$$, where $$x is $$the number of units sold (in hundreds). What is the profit if 300 units are sold?

Accepted Answer

$$P(3) = 5(3)^2$ - 20(3) + 100 = 45 - 60 + 100 = 85$$

Question 8

The height $$h (in $$meters) of a ball thrown upward is given by $$h(t) = -4.9t^2$ + 20t + 2$$, where $$t is $$time in seconds. What is the height after 3 seconds?

Accepted Answer

$$h(3) = -4.9(3)^2$ + 20(3) + 2 = -44.1 + 60 + 2 = 17.9$$

Question 9

If $$f(x) = x^2$ - 4x + 7$$, what is $$f(x + 2)$$?

Accepted Answer

Question 10

A population of bacteria is modeled by $$P(t) = 1000e$$^{0.2t}$$, where t$ is time in hours. What is the population after 5 hours?

Accepted Answer

$$P(5) = 1000e$$^{1}$$ \approx 2718$$

Question 11

If $$f(x) = 2x^2$ - 3x + 4$$, what is $$f(-x)$$?

Accepted Answer

$$2x^2 + 3x + 4$

Question 12

A car's position is modeled by $$s(t) = 4t^2$ + 2t + 1$$, where $$t is $$time in seconds. What is the position after 10 seconds?

Accepted Answer

$$s(10) = 4(10)^2$ + 2(10) + 1 = 400 + 20 + 1 = 421$$

Question 13

If $$f(x) = x^2$ - 6x + 8$$, what is $$f(x + 1)$$?

Accepted Answer

Question 14

A medication's concentration in the bloodstream is modeled by $$C(t) = 50e$$^{-0.5t}$$, where t$ is time in hours. What is the concentration after 4 hours?

Accepted Answer

$$C(4) = 50e$$^{-2}$$ \approx 6.77$$

Question 15

If $$f(x) = 3x^2$ - 2x + 1$$, what is $$f(2x + 1)$$?

Accepted Answer

$$12x^2 + 10x + 2$

Question 16

A chemical reaction's rate is modeled by $$R(t) = 8t^2$ - 5t + 2$$, where $$t is $$time in minutes. What is the rate after 6 minutes?

Accepted Answer

$$R(6) = 8(36) - 5(6) + 2 = 288 - 30 + 2 = 260$$

Question 17

If $$f(x) = x^2$ + 2x + 1$$, what is $$f(x - 2)$$?

Accepted Answer

$$x^2 - 4x + 5$

Question 18

A business models its revenue $$R(x) in $$thousands of dollars by $$R(x) = 10x^2$ - 15x + 50$$, where $$x is $$the number of products sold (in hundreds). What is the revenue if 400 products are sold?

Accepted Answer

$$R(4) = 10(4)^2$ - 15(4) + 50 = 160 - 60 + 50 = 150$$

Evaluating Functions and Function Notation: Precalculus Study Notes

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