Q: A parking garage charges $$2 for up to 1.5 hours, 4 $$for up to 3 hours, $$6 for up to 4.5 hours, and 8 $$for up to 10 hours. Which piecewise function correctly models the cost $$C(t)$$ for $$t$$ hours parked?

$$C(t) = \begin{cases} 2, & 0 \leq t \u003c 1.5 \\ 4, & 1.5 \leq t \u003c 3 \\ 6, & 3 \leq t \u003c 4.5 \\ 8, & 4.5 \leq t \leq 10 \end{cases}$$

Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{x+3}$$?

Accepted Answer

$$[-3, \infty)$$

Question 2

Given the function $$f(x) = 2x - 4$$, what is the zero of the function?

Accepted Answer

$$x = 2$$

Question 3

A parking garage charges $$2 for up to 1.5 hours, 4 $$for up to 3 hours, $$6 for up to 4.5 hours, and 8 $$for up to 10 hours. Which piecewise function correctly models the cost $$C(t)$$ for $$t$$ hours parked?

Accepted Answer

$$C(t) = \begin{cases} 2, & 0 \leq t \u003c 1.5 \ 4, & 1.5 \leq t \u003c 3 \ 6, & 3 \leq t \u003c 4.5 \ 8, & 4.5 \leq t \leq 10 \end{cases}$$

Question 4

Which of the following is the correct composition $$(f \circ g)(x) if$$ $$f(x) = x^2$ - x$$ and $$g(x) = 4 - x$$?

Accepted Answer

$$(f \circ g)(x) = (4 - x)^2$ - (4 - x)$$

Question 5

Suppose $$f(x) = x + 1$$ and $$g(x) = \sqrt{x + 3}. $$What is the domain of $$(f + g)(x)$$?

Accepted Answer

$$[-3, \infty)$$

Question 6

A stone is thrown into a pond, creating a circular ripple whose radius increases at $$3 ft/sec. $$What is the area of the ripple as a function of time $$t$$ seconds after the stone hits the pond?

Accepted Answer

$$A(t) = 9\pi t^2$

Question 7

Which transformation describes the function $$f(x) = |x - 2| - 3$$ compared to the basic function $$y = |x|$$?

Accepted Answer

Shift right 2 units and down 3 units

Question 8

If $$y$$ varies directly as $$x$$ and $$y = 12$$ when $$x = 3$$, what is the equation relating $$y$$ and $$x$$?

Accepted Answer

$$y = 4x$$

Question 9

Which of the following functions is symmetric with respect to the y-axis?

Accepted Answer

$$y = x^2$

Question 10

Given $$R(x) = 60x - 0.4x^2$ and C(x) = 4x + 32$, what is the profit function P(x$$)$$?

Accepted Answer

$$P(x) = 56x - 0.4x^2$ - 32$$

Question 11

Which of the following describes a vertical stretch of the function $$y = f(x) by a $$factor of 3?

Accepted Answer

$$y = 3f(x)$$

Question 12

If $$y$$ varies inversely as $$x$$ and $$y = 5$$ when $$x = 2$$, what is the value of $$y$$ when $$x = 10$$?

Accepted Answer

$$y = 1$$

Question 13

Which of the following is the correct formula for the composition $$K(t)$$ that converts Fahrenheit temperature $$t$$ directly to Kelvin, given $$c(t) = \frac{5}{9}(t-32)$$ and $$k(c) = c + 273$$?

Accepted Answer

$$K(t) = \frac{5}{9}(t-32) + 273$$

Question 14

Which of the following is the correct equation for a function with the shape of $$y = |x|$$, reflected across the x-axis and shifted 4 units left?

Accepted Answer

$$y = -|x + 4|$$

Question 15

The flow rate $$F of $$water from a fire hose varies directly with the pump pressure $$P$$ and inversely with the hose length $$L. If$$ $$F = 500$$ when $$P = 200$$ and $$L = 50$$, what is $$F$$ when $$P = 150$$ and $$L = 50$$?

Accepted Answer

$$F = 375$$

Question 16

Which of the following is the correct domain for the function $$h(x) = \sqrt{4 - x}$$?

Accepted Answer

$$(-\infty, 4]$$

Question 17

Which of the following describes the transformation $$f(x) = \sqrt{x+5} + 4$$ compared to $$y = \sqrt{x}$$?

Accepted Answer

Shift left 5 units and up 4 units

Question 18

If $$y$$ varies jointly as $$x$$ and $$z$$, and $$y = 24$$ when $$x = 2$$ and $$z = 3$$, what is the value of $$y$$ when $$x = 4$$ and $$z = 5$$?

Accepted Answer

$$y = 80$$

College Algebra Study Guide: Chapter 2 – More on Functions

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