Question 1

Given the graph of $$G(x) in $$Image 1, what is the domain of the function?

Accepted Answer

$$[-5, 5]$$

Question 2

Given the graph of $$h(z) in $$Image 2, what is the range of the function?

Accepted Answer

$$[-5, 9]$$

Question 3

For the function $$f(t) in $$Image 3, which of the following is true about the domain?

Accepted Answer

$$[-5, 5]$$ with $$t = -2$$ not included$

Question 4

For the function $$R(p) in $$Image 4, which $$p-$$value is NOT included in the domain?

Accepted Answer

$$p = 1$$

Question 5

Consider the function $$f(x) = \frac{1}{x-5}. $$Which input is not allowed and why?

Accepted Answer

$$x = 5$$, because the denominator becomes zero

Question 6

Find the domain of $$T(x) = \sqrt{x-3}.$$

Accepted Answer

$$[3, \infty)$$

Question 7

Find the domain of $$k(x) = \frac{1}{x^2$-9}.$$

Accepted Answer

$$(-\infty, -3) \cup (-3, 3) \cup (3, \infty)$$

Question 8

For the function $$f(x) = \sqrt{10-2x}$$, what is the domain?

Accepted Answer

$$(-\infty, 5]$$

Question 9

A pizza shop can make at most 200 pizzas per day. Each pizza sells for $$14. The revenue function is G(x) = 14x$. What is the practical domain?

Accepted Answer

$$[0, 200]$$

Question 10

A candle is 20 cm tall and burns at 2 cm per hour until it burns out. The height function is $$h(t) = 20 - 2t. $$What is the practical range?

Accepted Answer

$$[0, 20]$$

Question 11

A car accelerates from 0 to 60 mph in 8 seconds. The speed function is $$g(t) = 7.5t. $$What is the practical domain?

Accepted Answer

$$[0, 8]$$

Question 12

You bike at 12 mph and can ride at most 10 hours in a day. The distance function is $$d(t) = 12t. $$What is the practical range?

Accepted Answer

$$[0, 120]$$

Question 13

A window washing company charges $$1.00 per window plus a base fee of 20.00 $$per appointment. They can wash a maximum of 200 windows per appointment. What is the function for total cost $$C(t) in $$terms of windows washed $$t$$?

Accepted Answer

$$C(t) = t + 20$$

Question 14

Gas costs $$4/gallon$$ and your car has a 15-gallon tank. What is the domain of the function $$C(T) = 4T$$ where $$T is $$the number of gallons?

Accepted Answer

$$[0, 15]$$

Question 15

A function $$f$$ has domain $$[0, 10]$$ and range $$[2, 8]. Is$$ $$f(12)$$ defined?

Accepted Answer

No, because 12 is not in the domain

Question 16

A student claims, 'If the domain of a function is all real numbers, then the range must also be all real numbers.' Which of the following disproves this claim?

Accepted Answer

$$f(x) = x^2$ has domain $$(-\infty, \infty)$$ but range $$[0, \infty)$$

Question 17

Given the function $$y = \frac{6}{x^2$ - 3x + 3} ($$Image 6), what is the domain?

Accepted Answer

$$(-\infty, \infty)$$

College Algebra Study Guide: Domain and Range

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