Question 1

Which of the following equations represents a function? Justify your answer.

Accepted Answer

$$y = \sqrt{x}$$

Question 2

Given the equation $$6x + 2y = 4$$, what are the $$x- $$and $$y-$$intercepts?

Accepted Answer

$$x-$$intercept: $$(\frac{2}{3}, 0)$$, $$y-$$intercept: $$(0, 2)$$

Question 3

Solve for $$b in $$the equation $$\frac{b-1}{2} = b.$$

Accepted Answer

$$b = -1$$

Question 4

Given $$f(x) = 2x^2$ + 7x + 3$$, $$g(x) = \sqrt{2x + 1}$$, $$h(x) = 12$$, and $$k(x) = \frac{1}{x}$$, compute $$f(1) + g(12) + h(0) + k(2).$$

Accepted Answer

$$12 + 5 + 12 + 0.5 = 29.5$$

Question 5

What is the domain of $$g(x) = \sqrt{2x + 1}$$?

Accepted Answer

$$x \geq -0.5$$

Question 6

Find all real zeros of $$f(x) = 2x^2$ + 7x + 3.$$

Accepted Answer

$$x = -3,\ x = -0.5$$

Question 7

Write the equation of a line with $$y-$$intercept $$3$$ and $$x-$$intercept $$2.$$

Accepted Answer

$$y = -\frac{3}{2}x + 3$$

Question 8

John rents a car for $$200 plus 0.20 $$per mile driven. Which function models the total cost $$C$$ for $$m$$ miles, and what is the cost for 350 miles?

Accepted Answer

$$C(m) = 200 + 0.2m;\ C(350) = 270$$

Question 9

An oil company increased production from 1.3 million barrels in 2012 to 1.6 million barrels in 2015. What is the average rate of change per year?

Accepted Answer

$$0.1$$ million barrels per year

Question 10

Suppose India purchased 32,000 industrial robots in 2016, which is 60% more than the US purchased that year. How many did the US purchase?

Accepted Answer

$$20,000$$

Question 11

Two trains leave a station: the first at 9am at $$60 km/h$$, the second at 11am at $$80 km/h. At $$what time will the second train catch up to the first?

Accepted Answer

5pm

Question 12

Two runners, Alex and Brady, start on opposite ends of a $$30 km $$trail. Alex runs at $$9 km/h$$, Brady at $$7 km/h. $$How far will Alex have run when they meet?

Accepted Answer

$$16.875 km$$

Question 13

Solve the inequality $$4|3x - 1| \leq 16$$ and write your answer in interval notation.

Accepted Answer

$$[-1.25, 1.25]$$

Question 14

Given $$k(x) = \frac{1}{x}$$, what is the domain of $$k(x)$$?

Accepted Answer

$$x 
eq 0$$

Question 15

Find the equation of a line with slope $$2$$ and $$x-$$intercept $$6.$$

Accepted Answer

$$y = 2x - 12$$

Question 16

Given $$g(x) = \sqrt{2x + 1}$$, find all real zeros of $$g(x).$$

Accepted Answer

$$x = -0.5$$

Question 17

Solve for $$x$$: $$2(x-1) - 2(x-1) = 0.$$

Accepted Answer

All real numbers

Question 18

Given $$h(x) = 12$$, $$g(x) = \sqrt{2x + 1}$$, and $$k(x) = \frac{1}{x}$$, compute $$k(g(h(9))).$$

Accepted Answer

$$\frac{1}{5}$$

Question 19

Solve the inequality $$\frac{|x + 1|}{3} + 2 \u003e 305.$$

Accepted Answer

$$x \u003e 902 or$$ $$x \u003c -904$$

Question 20

Write the equation for a function $$g(x)$$ such that $$g(3) = 16$$ and $$g(1) = 5$$, assuming $$g(x) is $$linear.

Accepted Answer

$$g(x) = 5.5x - 0.5$$

College Algebra Exam I Practice Guidance

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드