Precalculus Midterm Exam Review

Front

What is the result of f(x) - g(x) if f(x) = 9 - 3x and g(x) = 5x - 7?

Back

f(x) - g(x) = -8x + 16.

Front

How much will Kennedy earn in total after 10 years if she invests $3,000 at an interest rate of 2.9% compounded quarterly?

Back

Total amount earned = $4005.09.

Front

If the graph of f(x) passes through (1, 4), what point does f^{-1}(x) pass through?

Back

f^{-1}(x) passes through (4, 1).

Front

Solve for x: log_2(x + 2) + log_2(x) = 3.

Back

x = 2.

Front

What is an example of a cubic monomial?

Back

5x^3 is a cubic monomial.

Front

Define a function.

Back

A function is a relation that assigns exactly one output for each input.

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has the form f(x) = mx + b, while a quadratic function has the form f(x) = ax^2 + bx + c.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements.

Front

What is the formula for compound interest?

Back

A = P(1 + r/n)^{nt}, where A is the amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Front

What is the inverse of a function?

Back

The inverse of a function f(x) is a function f^{-1}(x) that reverses the effect of f(x).