Free Printable Unit 8 Learning Check

1.

If $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then $\left(f+g\right)\left(x\right)=$

a)

$5x^2+1$

b)

$5x^2-3$

c)

$6x+1$

d)

$6x-3$

2.

If $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then $\left(f-g\right)\left(x\right)=$

a)

-4x - 3

b)

-4x +1

c)

6x + 1

d)

6x - 3

3.

If $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then $\left(f\cdot g\right)\left(x\right)=$

a)

$5x-3$

b)

$5x^2+2$

c)

$5x^2-7x+2$

d)

$5x-7$

4.

If $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then $\left(\frac{f}{g}\right)\left(x\right)$

a)

$\frac{x-1}{5x-2}$

b)

$\frac{5x-2}{x-1}$

c)

$\frac{-1}{3}$

d)

$-3$

5.

If $f\left(x\right)\ =\ 3x^2-4$ and $g\left(x\right)=x^2-8x+4$ , then $\left(f+g\right)\left(x\right)=$

a)

$4x^4-8x-8$

b)

$4x^4-8x$

c)

$4x^2-8x-8$

d)

$4x^2-8x$

6.

If $f\left(x\right)\ =\ 3x^2-4$ and $g\left(x\right)=x^2-8x+4$ , then $\left(f-g\right)\left(x\right)=$

a)

$2x^2-8x-8$

b)

$2x^2+8x-8$

c)

$2x^2-8x$

d)

$2x^2+8x$

7.

If $f\left(x\right)\ =\ 3x^2-4$ and $g\left(x\right)=x^2-8x+4$ , then $\left(f\cdot g\right)\left(x\right)=$

a)

$3x^4-24x^3+8x^2+32x-16$

b)

$3x^4-8x-16$

c)

$3x^4-24x^3+8x^2-32x-16$

d)

$3x^4-24x^3+16x^2+32x-16$

8.

If $f\left(x\right)\ =\ 3x^2-4$ and $g\left(x\right)=x^2-8x+4$ , then $\left(\frac{f}{g}\right)\left(x\right)=$

a)

$\frac{3x^2-4}{x^2-8x+4}$

b)

$\frac{x^2-8x+4}{3x^2-4}$

c)

$\frac{3x^2-1}{x^2-8x}$

d)

$\frac{1}{-4x}$

9.

If $f\left(x\right)\ =\ x+5$ and $g\left(x\right)=3x-7$ , then $\left(f\circ g\right)\left(x\right)=$

a)

$3x-2$

b)

$3x+8$

c)

$3x^2+8x-35$

d)

$3x-12$

10.

If $f\left(x\right)\ =\ x+5$ and $g\left(x\right)=3x-7$ , then $\left(g\circ f\right)\left(x\right)=$

a)

$3x-2$

b)

$3x+8$

c)

$3x^2+8x-35$

d)

$3x-12$

11.

If $f\left(x\right)\ =\ x^2+6x-2$ and $g\left(x\right)=x-6$ , then $\left(f\circ g\right)\left(x\right)=$

a)

$x^2-6x+34$

b)

$x^2-6x-2$

c)

$x^2+6x-8$

d)

$x^2+6x-2$

12.

If $f\left(x\right)\ =\ x^2+6x-2$ and $g\left(x\right)=x-6$ , then $\left(g\circ f\right)\left(x\right)=$

a)

$x^2-6x+34$

b)

$x^2-6x-2$

c)

$x^2+6x-8$

d)

$x^2+6x+12$

13.

If $f\left(x\right)=5x$ , $g\left(x\right)=-2x+1$ , and $h\left(x\right)=x^2+6x+8$ , find $f\left(g\left(-2\right)\right)$ . (Your answer should be a number.)

(a)

14.

If $f\left(x\right)=5x$ , $g\left(x\right)=-2x+1$ , and $h\left(x\right)=x^2+6x+8$ , find $h\left(f\left(-5\right)\right)$ . (Your answer should be a number.)

(a)

15.

Find the domain of each function.

f\left(x\right)=\frac{3x}{x+3}

a)

$\left(-\infty,\ 3\right)∪\left(3,\infty\right)$

b)

$\left(-\infty,0\right)∪\left(0,\infty\right)$

c)

$\left(-\infty,\ -3\right)∪\left(-3,\infty\right)$

d)

$\left(-\infty,\ -3\right)∪\left(0,\infty\right)$

16.

Find the domain of the function.

f\left(x\right)=\frac{x+3}{5x}

a)

$\left(-\infty,\ -3\right)∪\left(-3,\ \infty\right)$

b)

$\left(-\infty,5\right)\ ∪\ \ \left(5,\infty\right)$

c)

$\left(-\infty,0\right)∪\left(0,\infty\right)$

d)

$\left(-\infty,\ -1\right)∪\left(-1,\infty\right)$

17.

Find the domain of

f\left(x\right)\ =\ x-3

a)

$\left(-\infty,\ \infty\right)$

b)

$\left(-\infty,3\right)\cup\left(3,\infty\right)$

c)

$\left(-\infty,-4\right)\cup\left(-4,\infty\right)$

d)

$\left(-\infty,-4\right)\cup\left(-4,3\right)\cup\left(3,\infty\right)$

18.

Find the domain of each function.

f\left(x\right)=\sqrt{3x-21}

a)

$\left[7,\infty\right]$

b)

$\left[3,\infty\right)$

c)

$\left[7,\infty\right)$

d)

$\left[21,\infty\right)$

19.

Find the domain of each function.

f\left(x\right)=\sqrt{8x+40}

a)

$\left[-5,\infty\right]$

b)

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

c)

$\left[-5,\infty\right)$

d)

$\left[5,\infty\right)$

20.

Find the domain of each function.

f\left(x\right)=x^2-6x+8

a)

$\left(-\infty,2\right)∪\left(-4,\ 2\right)\cup\left(-4,\infty\right)$

b)

$\left(-\infty,-4\right)∪\left(-4,\ -2\right)\cup\left(-2,\infty\right)$

c)

$\left(-\infty,2\right)∪\left(2,\ 4\right)\cup\left(4,\infty\right)$

d)

$\left(-\infty,\ \infty\right)$

21.

Find the domain of h(x):

a)

(- ∞, ∞)

b)

[2, ∞)

c)

(-∞, -2]

d)

[-2, ∞)

22.

Find the domain of the function: $f(x)=\frac{x}{2x+4}$

a)

$\left(-\infty,\ 2\right)\cup\left(2,\ \infty\right)$

b)

$\left(-\infty,\ 4\right)\cup\left(4,\ \infty\right)$

c)

$\left(-\infty,\ -2\right)\cup\left(-2,\ \infty\right)$

d)

$\left(-\infty,\ \infty\right)$

23.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

24.

Find the inverse of the function
f(x) = 3x − 5

a)

f^-1(x)=3x +5

b)

f^-1(x)=(x+5)/3

c)

f^-1(x)=3y-5

d)

f^-1(x)=3y+5

25.

a)

Inverse Functions

b)

Not Inverse Functions

26.

Are the following inverses of each other? Use composition of functions. fog(x) and gof(x)

a)

True

b)

False

27.

What is the inverse of the points (1,3)(2,4)(6,2)

a)

(2,6)(3,1)(4,2)

b)

(-3,-1)(-4,-2)(-2,-6)

c)

(1,3)(2,4)(6,2)

d)

(-1,-3)(-2,-4)(-6,-2)

28.

What does it mean to find the inverse of a function?

a)

the x's and y's are switched

b)

the x's and y's are divided by 2

c)

the x's and y's are made negative

d)

the x's and y's are the same

29.

Find the inverse
f(x)= x⁴- 2

a)

∜(x+2)

b)

(x+2)⁴

c)

-1+2x⁴

d)

∜2x

30.

Solve for the inverse of the following.

a)

$y=\left(x+5\right)^2$

b)

$y=x+25$

c)

$y=\left(x-5\right)^2$

d)

$y=x^2+5$

31.

Solve for the inverse of the following.

a)

$y=\left(x+1\right)^2$

b)

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

c)

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

d)

$y=\left(x-1\right)^2$

32.

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

a)

$\frac{x}{3}$

b)

$\frac{3}{x}$

c)

$0.3x$

d)

$x\times3$

Unit 8 Learning Check

Total questions: 32

Worksheet time: 6hrs 25mins

Similar Resources on Wayground