Quiz about 2024 College Algebra Final

Question 1

Use the vertical line test to determine which graph represents a relation that is a function.

Accepted Answer

Question 2

Find the domain of the function $$f(x)=\frac{x+12}{x^2+7x-18}$$

Accepted Answer

$$(−∞,−9)∪(−9,2)∪(2,∞)$$

Answer

$$(−∞,−9)\cup(2,∞)$$

Answer

$$(−∞,2)∪(2,∞)$$

Answer

$$(−∞,−9)∪(−9,∞)$$

Question 3

Give the domain of $$h\left(x\right)=\sqrt[]{-10-x}$$ in inequality notation.

Accepted Answer

$$x\le-10$$

Answer

$$x\ge-10$$

Answer

All real numbers

Answer

$$x
e-10$$

Question 4

Given the functions: $$f\left(x\right)=6x+4$$ and $$g\left(x\right)=x^2+10x-7$$ , find $$\left(f-g\right)\left(x\right)$$ .

Accepted Answer

$$-x^2-4x+11$$

Answer

$$-x^2+12x+2$$

Answer

$$-x^2+8x+10$$

Answer

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

Question 5

Given the functions: $$f\left(x\right)=6x+6$$ and $$g\left(x\right)=x^2+10x-7$$ , find $$\left(f\cdot g\right)\left(x\right)$$

Accepted Answer

$$6x^3+66x^2+18x-42$$

Answer

$$6x^3+26x^2-28x-24$$

Answer

$$x^3+26x^2-24x+28$$

Answer

$$26x^3+10x^2-24x-28$$

Question 6

Given that $$f\left(x\right)=x^2-7x$$ and $$g\left(x\right)=x+3$$ , calculate $$\left(fo\ g\right)\left(x\right)$$ .

Accepted Answer

$$\left(x+3\right)^2-7\left(x+3\right)$$

Answer

$$\left(x^2-7x\right)+3$$

Answer

$$x^2+3x+x-7$$

Answer

$$\left(x-7\right)^2+3\left(x-7\right)$$

Question 7

Given the function $$f\left(x\right)=3x-5$$ , which one of the following is the formula for the inverse function $$f^{-1}.$$

Accepted Answer

$$f^{-1}\left(x\right)=\frac{x+5}{3}$$

Answer

$$f^{-1}\left(x\right)=\frac{5}{3}x+\frac{3}{5}$$

Answer

$$f^{-1}\left(x\right)=5x-3$$

Answer

$$f^{-1}\left(x\right)=-5x-3$$

Question 8

Which of the following functions match this graph?

Accepted Answer

$$𝑓(𝑥)=|𝑥+3|+1$$

Answer

$$𝑓(𝑥)=|𝑥+1|−3$$

Answer

$$𝑓(𝑥)=|𝑥-3|+1$$

Answer

$$𝑓(𝑥)=|𝑥-1|−3$$

Question 9

Determine the vertex of the quadratic function $$y=x^2-10x+19$$

Accepted Answer

$$(5,-6)$$

Answer

$$\left(5,6\right)$$

Answer

$$\left(-5,0\right)$$

Answer

$$\left(-5,25\right)$$

Question 10

Find the x-intercepts of the graph of the function $$y=-2x^2+7x+3$$

Accepted Answer

$$x=\frac{-7\pm\sqrt[]{73}}{-4}$$

Answer

$$x=\frac{-7\pm\sqrt[]{73}}{4}$$

Answer

$$x=\frac{7\pm\sqrt[]{73}}{-2}$$

Answer

$$x=\frac{7\pm\sqrt[]{25}}{-4}$$

Question 11

A ball is launched upward at 64 feet/second from a platform that is 140 feet high. The equation giving its height t seconds after launch is $$h\left(t\right)=-16t^2+64t+140$$ . About how long does it take for the ball to hit the ground?

Accepted Answer

5.6 seconds

Answer

5.6 seconds or 1.6 seconds

Answer

1.6 seconds

Answer

4 seconds

Question 12

Match the function $$f\left(x\right)=3\left(x-2\right)^2$$ with its graph.

Accepted Answer

Question 13

Identify whether the graph represents a polynomial function that has a degree that is even or odd, and whether the leading term is positive or negative.

Accepted Answer

odd and leading term is negative

Answer

even and leading term is positive

Answer

odd and leading term is positive

Answer

even and leading term is negative

Question 14

Find the quotient and remainder using synthetic division for

Accepted Answer

Quotient: $$x^2+x+7$$

Remainder: 2

Answer

Quotient: $$x^2+x+7$$

Remainder: -14

Answer

Quotient: $$x^2+3x+9$$

Remainder: 16

Answer

Quotient: $$-2x-10$$

Remainder: -8

Question 15

Find all zeros of $$f\left(x\right)=x^3+x^2+x+1$$

Accepted Answer

$$-1,i,-i$$

Answer

$$-1,1+i,1-i$$

Answer

$$1,i,-i$$

Answer

$$4,-1,0$$

Question 16

Find all the solutions of the equation $$x^4-13x^2+36=0$$

Accepted Answer

$$x=\pm2,x=\pm3$$

Answer

$$x=\pm4,x=\pm9$$

Answer

$$x=2,x=3$$

Answer

$$x=0,x=36$$

Question 17

Determine the equations of the vertical and horizontal asymptotes for the rational function

$$f\left(x\right)=\frac{2x-4}{2x+4}$$

Accepted Answer

Vertical Asymptote:

x = - 2

Horizontal Asymptote: y = 1

Answer

Vertical Asymptote:

x = - 2

Horizontal Asymptote: y = 2

Answer

Vertical Asymptote:

x = - 1

Horizontal Asymptote: y = -2

Answer

Vertical Asymptote:

x = 0

Horizontal Asymptote: y = 0

Question 18

You deposit $13,000 in an account earning 8% compounded weekly for 4 years. How much interest was earned?

Accepted Answer

$4,898.26

Answer

$346.67

Answer

$4,100.00

Answer

$1,040.71

Question 19

You've just inherited $11,000. You will be investing the $11,000 at 6% compounded continuously. Find the future value of the account, if you invest the money for 8 years.

Accepted Answer

$$\$17,776.82$$

Answer

$$\$18,776.82$$

Answer

$$\$1,336,614.59$$

Answer

$$\$16,280.00$$

Question 20

Select the graph of the function.

$$f\left(x\right)=\frac{\left(x-4\right)}{\left(x-2\right)\left(x+1\right)}$$

Accepted Answer

Question 21

Find an equation for the graph sketched below

Accepted Answer

$$y=3\left(2^x\right)$$

Answer

$$y=3^x$$

Answer

$$y=2\left(\frac{1}{3}\right)^x$$

Answer

$$y=\log_{ }x$$

Question 22

Which sequence of transformations will yield the graph of $$g\left(x\right)=8^{\left(x-9\right)}-4$$

Accepted Answer

Horizontal shift 9 units to the right;

Vertical shift 4 units down

Answer

Horizontal shift 9 units to the left; Vertical shift 4 units up

Answer

Horizontal shift 4 units to the left; Vertical shift 9 units up

Answer

Horizontal shift 4 units to the right; Vertical shift 9 units down

Question 23

Choose the graph of $$y=\log_3\left(x-4\right)$$

Accepted Answer

Question 24

Which of the following is equivalent to the expression

$$\log_{ }\left(\frac{x^{13}y^5}{\sqrt[]{z}}\right)$$

Accepted Answer

$$13\log\left(x\right)+5\log\left(y\right)-\frac{1}{2}\log\left(z\right)$$

Answer

$$13\log\left(x\right)+5\log\left(y\right)+\frac{1}{2}\log\left(z\right)$$

Answer

$$18\log\left(xy\right)-\frac{1}{2}\log\left(z\right)$$

Answer

$$\frac{37}{2}\log\left(\frac{xy}{z}\right)$$

Question 25

Solve the equation: $$\log_4\left(x-15\right)=2$$

Accepted Answer

$$x=31$$

Answer

$$x=12$$

Answer

$$x=14$$

Answer

$$x=9$$

Question 26

Solve the following exponential equation $$43\left(e^{0.92x}\right)=34$$ . Round your answer to three decimal places.

Accepted Answer

$$x=-0.255$$

Answer

$$x=-2.172$$

Answer

$$x=-1.874$$

Answer

$$0.754$$

Question 27

Find the inverse of

Accepted Answer

Answer

Impossible

Question 28

Question 28.

Accepted Answer

Answer

Impossible

Question 29

Question 29.

Accepted Answer

Impossible

Answer

Answer

Answer

Question 30

Solve the system of equations by converting to a matrix equation and using the inverse of the coefficient matrix.

Accepted Answer

$$x=16,y=91$$

Answer

$$x=95,y=96$$

Answer

$$x=-5671,y=4839$$

Answer

$$x=-7,y=-4$$

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