Free Printable Make up DOL Mixed Problems

1.

Find the mistake

$step\ 1\ f\left(x\right)=-3\log\left(-x-6\right)+12$

$step\ 2\ \ \ \ y=-3\log\left(-x-6\right)+12$

$step\ 3\ \ \ \ \ x=-3\log\left(-y-6\right)+12$

$step\ 4\ \ \ \ \ x-12=-3\log\left(-y-6\right)$

$step\ 5\ \ \ \ -\frac{1}{3}x-4=\log\left(-y-6\right)$

$step\ 6\ \ \ \ 10^{-\frac{1}{3}x-4}=-y-6$

$step\ 7\ \ \ \ f^{-1}\left(x\right)=-10^{-\frac{1}{3}x-4}-6$

a)

Step 2

b)

step 3

c)

step 4

d)

step 5

e)

To see all the steps scroll up and down.

2.

Find the inverse of $f\left(x\right)=-4\left(5\right)^{x-7}+12$

a)

$f^{-1}\left(x\right)=\log_5\left(-\frac{1}{4}x+3\right)+7$

b)

$f^{-1}\left(x\right)=7\log_5\left(-\frac{1}{4}x+3\right)$

c)

$f^{-1}\left(x\right)=\log_5\left(x-3\right)-7$

3.

In the general log function
y = a*log_b(x-h)+k, what letter tells us if the function has moved left or right?

a)

a

b)

b

c)

h

d)

k

4.

Select all the transformations that apply.

y = 5log₂(x)

a)

Vertical stretch

b)

Vertical Compression

c)

Horizontal compression

d)

Horizontal stretch

5.

What is the transformation?

a)

Vertical Translation up 2 and Horizontal translation right 1

b)

Vertical Translation down 2 and Horizontal Translation left 1

c)

Horizontal Translation left 2 and Vertical Translation up 1

d)

Horizontal Translation right 2 and Vertical Translation down 1

6.

What is the transformation?

a)

Right 3 and Up 7

b)

Left 3 and Up 7

c)

Right 3 and Down 7

d)

Left 3 and Down 7

7.

$Log_32x=5$ can be rewritten as...

a)

$2x=3^5$

b)

$5=3^{2x}$

c)

$2x=5^3$

8.

$Log4x=2$ can be rewritten as...

a)

$4x=10^2$

b)

$2=10^{4x}$

c)

$10=4^{6x}$

9.

Which of the following is the correct first two steps when solving for x

$\log_7\left(x-3\right)+\log_7\left(x+1\right)=1$

a)

$\log_7\left(x^2-2x-3\right)=1$ $x^2-2x-3=7^1$

b)

$x^2-2x-3=1$ $x^2-2x-2=0$

c)

$\log_7\left(x^2-2x-3\right)=1$ $7^{x^2-2x-3}=1$

d)

$\log_7\left(1\right)=x^2-2x-3$ $\log_7\left(x^2-2x-3\right)=1$

10.

Solve for x. $\log_8\left(x\right)+\log_8\left(x+2\right)=1$

a)

2, 13

b)

13

c)

2

d)

Hint: When you add logs into one log, multiply the inside. Then rewrite the log as a power to solve.

Make up DOL Mixed Problems

Total questions: 10

Worksheet time: 22mins

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