4.1-4.2 Review (Pre-Calc)

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input. It passes both the vertical line test and the horizontal line test.

Front

What does the vertical line test determine?

Back

The vertical line test determines if a graph represents a function. If any vertical line crosses the graph more than once, it is not a function.

Front

What does the horizontal line test determine?

Back

The horizontal line test determines if a function is one-to-one. If any horizontal line crosses the graph more than once, the function is not one-to-one.

Front

How do you find the inverse of a function?

Back

To find the inverse of a function, swap the x and y variables and solve for y.

Front

If f(x) = 3x - 9, what is f^(-1)(12)?

Back

f^(-1)(12) = 7.

Front

What is the growth rate in the function y = 4(1.2)^x?

Back

The growth rate is 20%.

Front

What transformations occur in g(x) = -2^(x+3) - 6 from f(x) = 2^x?

Back

The transformations are reflection over the x-axis, left 3 units, and down 6 units.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, often represented by a function of the form y = a(1 - r)^t.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is y = a(1 - r)^t, where a is the initial amount, r is the decay rate, and t is time.

Front

How do you calculate the value of an asset after a certain time with exponential decay?

Back

Use the formula V = P(1 - r)^t, where V is the value after time t, P is the initial value, r is the decay rate, and t is time.