Free Printable 2024 College Algebra Final

1.

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

a)

b)

c)

d)

2.

Given the function $f\left(x\right)=6x^2+6x-7$ ,

determine 𝑓(−4) .

a)

𝑓(−4) = 127

b)

𝑓(−4) = 65

c)

𝑓(−4) = 27

d)

𝑓(−4) = 91

3.

The function 𝑓(𝑥) is represented below as a graph. Find 𝑓(4)

a)

𝑓(4) = 1

b)

𝑓(4) = 3

c)

𝑓(4) = 2.42

d)

𝑓(4) = 0

4.

Given the piecewise function below, find 𝑓(1).

a)

𝑓(1) = −8

b)

𝑓(1) = 19

c)

𝑓(1) = 12

d)

𝑓(1) = 9

5.

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

a)

$(−∞,−9)\cup(2,∞)$

b)

$(−∞,2)∪(2,∞)$

c)

$(−∞,−9)∪(−9,∞)$

d)

$(−∞,−9)∪(−9,2)∪(2,∞)$

6.

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

a)

$x\ge-10$

b)

All real numbers

c)

$x\le-10$

d)

$x\ne-10$

7.

Determine the domain and range of the function using the graph below:

a)

Domain: (-1,2)

Range: (-2,2)

b)

Domain: [-2,2]

Range: [-1,2]

c)

Domain: [-1,2]

Range: [-2,2]

d)

Domain: (−∞, ∞)

Range: (−∞, 2]

8.

Consider the function in the graph below. Determine the intervals of increase and decrease.

a)

Increase: $(−∞,−5)𝑈(0,∞)$

Decrease: $(5,0)$

b)

Increase: (−5,1)

Decrease:

(−8, −5)𝑈(0, −7)

c)

Increase: (-5,0)

Decrease:

(−∞, −5)𝑈(0, ∞)

d)

Increase: [5,0]

Decrease:

(−∞, −5)𝑈(0, ∞)

9.

Determine the average rate of change for $f\left(x\right)=-x^2+4x$ between 𝑥 = 2 and 𝑥 = 4.

a)

-2

b)

1/2

c)

8

d)

1/8

10.

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

a)

$-x^2+12x+2$

b)

$-x^2+8x+10$

c)

$-x^2-4x+11$

d)

$x^2+12x+2$

11.

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

a)

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

b)

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

c)

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

d)

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

12.

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

a)

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

b)

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

c)

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

d)

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

13.

Use the graphs below to evaluate the expressions 𝑔(𝑓(5))

a)

𝑔(𝑓(5)) = 1

b)

𝑔(𝑓(5)) = 3

c)

𝑔(𝑓(5)) = 2

d)

𝑔(𝑓(5)) = 4

14.

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

a)

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

b)

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

c)

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

d)

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

15.

Which of the following functions match this graph?

a)

$𝑓(𝑥)=|𝑥+1|−3$

b)

$𝑓(𝑥)=|𝑥-3|+1$

c)

$𝑓(𝑥)=|𝑥-1|−3$

d)

$𝑓(𝑥)=|𝑥+3|+1$

16.

Given a line with slope = −6 and passing through (−5,4) , which of the following is the correct point-slope equation of the line?

a)

𝑦 − 4 = −5(𝑥 − 6)

b)

𝑦 + 4 = −6(𝑥 − 5)

c)

𝑦 − 4 = −6(𝑥 + 5)

d)

𝑦 + 4 = −6(𝑥 − 5)

17.

A company discovers that to produce 𝑥 = 740 new electronic parts, it will cost 𝑦 = $46,840. To produce x=620 new electronic parts, it will cost y=$40,120. Compute the average rate of change of the cost and choose the most accurate statement from the following:

a)

Cost is decreasing at a rate of $56 per item.

b)

Cost is increasing at a rate of $56 per item.

c)

Cost is decreasing at a rate of $91 per item

d)

Cost is increasing at a rate of $94 per item.

18.

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

a)

$(5,-6)$

b)

$\left(5,6\right)$

c)

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

d)

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

19.

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

a)

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

b)

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

c)

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

d)

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

20.

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?

a)

5.6 seconds

b)

5.6 seconds or 1.6 seconds

c)

1.6 seconds

d)

4 seconds

21.

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

a)

b)

c)

d)

22.

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.

a)

even and leading term is positive

b)

odd and leading term is positive

c)

even and leading term is negative

d)

odd and leading term is negative

23.

Find the quotient and remainder using synthetic division for

a)

Quotient: $x^2+x+7$

Remainder: -14

b)

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

Remainder: 16

c)

Quotient: $x^2+x+7$

Remainder: 2

d)

Quotient: $-2x-10$

Remainder: -8

24.

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

a)

$-1,i,-i$

b)

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

c)

$1,i,-i$

d)

$4,-1,0$

25.

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

a)

$x=\pm4,x=\pm9$

b)

$x=\pm2,x=\pm3$

c)

$x=2,x=3$

d)

$x=0,x=36$

26.

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

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

a)

Vertical Asymptote:

x = - 2

Horizontal Asymptote: y = 2

b)

Vertical Asymptote:

x = - 1

Horizontal Asymptote: y = -2

c)

Vertical Asymptote:

x = 0

Horizontal Asymptote: y = 0

d)

Vertical Asymptote:

x = - 2

Horizontal Asymptote: y = 1

27.

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

a)

$346.67

b)

$4,100.00

c)

$4,898.26

d)

$1,040.71

28.

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.

a)

$\$18,776.82$

b)

$\$1,336,614.59$

c)

$\$16,280.00$

d)

$\$17,776.82$

29.

Select the graph of the function.

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

a)

b)

c)

d)

30.

Find an equation for the graph sketched below

a)

$y=3^x$

b)

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

c)

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

d)

$y=\log_{ }x$

31.

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

a)

Horizontal shift 9 units to the right;

Vertical shift 4 units down

b)

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

c)

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

d)

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

32.

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

a)

b)

c)

d)

33.

Certain radioactive material decays in such a way that the mass remaining after 𝑡 years is given by the function $𝑚(𝑡)=465𝑒^{-0.045t}$ where 𝑚(𝑡) is measured in grams. How much of the mass remains after 10 years?

a)

1391.42 grams

b)

296.5 grams

c)

38.02 grams

d)

192.11 grams

34.

Which of the following is equivalent to the expression

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

a)

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

b)

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

c)

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

d)

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

35.

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

a)

$x=12$

b)

$x=14$

c)

$x=31$

d)

$x=9$

36.

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

a)

$x=-0.255$

b)

$x=-2.172$

c)

$x=-1.874$

d)

$0.754$

37.

Find the inverse of

a)

b)

c)

d)

Impossible

38.

a)

b)

c)

d)

Impossible

39.

a)

b)

c)

d)

Impossible

40.

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

a)

$x=95,y=96$

b)

$x=16,y=91$

c)

$x=-5671,y=4839$

d)

$x=-7,y=-4$

2024 College Algebra Final

Total questions: 40

Worksheet time: 40mins

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