Question 1

Evaluate the function $$f(x) = \frac{x^2$ - 4}{x - 2} at$$ $$x = 3$$ and simplify.

Accepted Answer

$$5$$

Question 2

Given the graph showing the percentage of students enrolled in the College of Engineering at State University, what is the approximate percentage in the year 1997?

Accepted Answer

Approximately $$23\%$$

Question 3

For the function $$f(x) = \sqrt{x} - 2$$, what is $$f(10)$$ and what does it represent in a real-world context?

Accepted Answer

$$1.16$$, representing the difference between the square root of $$10$$ and $$2$$

Question 4

Use the graph below to determine the domain and range. Is the graph a function?

Accepted Answer

Domain: $$(-\infty, 4]$$, Range: $$[0, \infty)$$, Yes, it is a function.

Question 5

Find and simplify the difference quotient for the function $$f(x) = x^2$ + 4.$$

Accepted Answer

$$2x + h$$

Question 6

Write the equation of the line in point-slope form passing through $$(3, 5)$$ and $$(6, 8).$$

Accepted Answer

$$y - 5 = 1(x - 3)$$

Question 7

Graph the equation $$y = \frac{1}{2}x + 1 in a $$rectangular coordinate system. What is the slope and y-intercept?

Accepted Answer

Slope: $$\frac{1}{2}$$, y-intercept: $$1$$

Question 8

The average value of a certain type of automobile was $$14,760 in$$ $$1995$$ and depreciated to $$4440 in$$ $$1999. $$What is the average rate of depreciation per year?

Accepted Answer

$$-3320$$ per year

Question 9

Use the given conditions to write an equation for the line in slope-intercept form passing through $$(2, 3)$$ and perpendicular to the line $$y = 2x + 8.$$

Accepted Answer

$$y - 3 = -\frac{1}{2}(x - 2)$$

Question 10

Find the average rate of change of the function $$f(x) = \sqrt{x}$$ from $$x = 2 to$$ $$x = 8.$$

Accepted Answer

$$\frac{\sqrt{8} - \sqrt{2}}{8 - 2}$$

Question 11

Along with incomes, people's charitable contributions have steadily increased over the past several years. The table below shows the average charitable contribution amounts for selected years. Find the average rate of annual increase between $$1991$$ and $$1995.$$

Accepted Answer

$$528$$ per year

Question 12

For $$f(x) = x^4$ + 2x - 2$$ and $$g(x) = x^2$ - 2x - 4$$, find the composition $$f(g(x - 2)).$$

Accepted Answer

$$((x - 2)^2$ - 2(x - 2) - 4)^4$ + 2((x - 2)^2$ - 2(x - 2) - 4) - 2$$

Question 13

Express the function $$h(x) = e$$^{x^2}$$ - x^4$ as a composition of two functions f$ and g$ so that h(x) = f(g(x$$))$$.

Accepted Answer

$$f(x) = e^x - x^2$, g(x$$) = $$x^2$$

Question 14

The function $$f(x) = (x + 1)^7$ is one-to-one. Find an equation for f$$^{-1}$$(x)$$, the inverse function.

Accepted Answer

$$f^{-1}(x$$) = $$x^{1/7} - 1$

Question 15

A company’s revenue $$R (in $$thousands of dollars) is modeled by $$R(x) = 2x + 8$$, where $$x is $$the number of years since 2010. What is the revenue in 2015?

Accepted Answer

$$18$$ thousand dollars

Question 16

If $$f(x) = x^2$ + 4$$ and $$g(x) = x - 2$$, what is $$f(g(5))$$?

Accepted Answer

$$25$$

Question 17

Which of the following best describes the graph of $$y = \frac{1}{2}x + 1$$?

Accepted Answer

A straight line with a positive slope and y-intercept at $$1$$

Question 18

Given the function $$f(x) = \sqrt{x}$$, which interval is the domain of $$f$$?

Accepted Answer

$$[0, \infty)$$

College Algebra: Unit 1 Exam Review Study Notes

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