Unit #3 CE College Algebra Review

Inverse Functions

100

Is the function y = 1/2x - 5 a one-to-one function? Explain

Yes. It is always increasing or it passes the horizontal line test.

200

The inverse of the function y = 8x+5.

What is y = (x-5)/8?

300

Three ordered pairs on the inverse function of the function that includes (1,2), (4, -3), and (-5,-8).

What are (2, 1), (-3, 4) and (-8,-5)?

400

Show that f(x)=x⁵ +1 and g(x)=(x-1)^(1/5) are inverse functions.

Show f(g(x))=x and g(f(x))=x.

500

The inverse of the function g(x)=log₂(x-1) + 3.

What is g^-1(x)=2^x-3 + 1?

Bonus, what is the domain of g^-1(x)?

Graphs of Logarithmic and Exponential Functions

100

The domain and range of the function y=3^x.

What is domain: (-infinity, infinity) and range: (0, infinity)?

200

The equation of the asymptote for the function y=log_1/2x.

What is x = 0?

300

The equation of the asymptote for the function g(x)=4^x + 2.

What is y = 2?

400

Describe the transformations of the graph g(x)=-log₃(x+1) and what changes would need to be made to the ordered pairs in a table.

Reflect in the x-axis: change the sign of all y-values.

Translate one left: subtract 1 from all of the x-values

500

Graph the function f(x)=-log₃(x+1)

https://www.desmos.com/calculator/1jdyzahctm

Solve Exponential Equations

100

The value of x in the equation 5^x=(1/25).

What is x=-2?

200

The value of x in the equation 2^2x-4=8^x+1.

What is x = -7?

300

The value of x, rounded to three decimal places, in the equation 20^x=60.

What is x = 1.367?

400

The value of x, rounded to 3 decimal places, in the equation 4^x-5=3.

What is x=5.792?

500

The value of x, rounded to three decimal places, in the equation 4(1.2)^x+1=24.

What is x= 8.827?

Solve Logarithmic Equations

100

The value of log₄64.

What is 3?

200

The value of x in the equation log_1/2x=-3.

What is 8?

300

The EXACT value of x in the equation 5lnx=20.

What is e⁴?

400

The value of x in the equation log₅(x-7)=2.

What is x=32?

500

The value of x in the equation log₇(x+4)+log₇(x-4)=log₇5.

What is x = 6?

Exponential Applications

100

How much $4000 grows to in an account that compounds interest quarterly at a rate of 3.5% for 7 years.

What is $5,105.04?

200

How many grams of carbon-14 are left after 3000 years for the following function y(t)=1000e^-0.0001216t. Round to three decimal places.

What is 694.336 grams?

Bonus, what was the initial amount of carbon-14 in the situation modeled by this equation?

300

How long it takes for 500 grams to become 125 grams for a function that decays exponentially according to the function y = 500e^-0.025t. Round to the nearest tenth of a year.

What is 55.5 years?

400

The amount of time, to the nearest tenth of a year, that it takes money to double in an account that compounds interest continuously at 4.2% interest.

What is 16.5 years?

500

The half-life of a substance whose exponential decay can be modeled by y=500e^-0.04t, to the nearest year.

What is 17 years?