Practice-Transformations and Exponential Equations

Front

What is a transformation in mathematics?

Back

A transformation is a function that maps a set of points to another set of points, altering their position, size, or orientation.

Front

What is a vertical translation?

Back

A vertical translation moves a graph up or down without changing its shape.

Front

What is a horizontal translation?

Back

A horizontal translation moves a graph left or right without changing its shape.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches infinity or negative infinity.

Front

How do you find the horizontal asymptote of an exponential function?

Back

For exponential functions of the form f(x) = a * b^x, the horizontal asymptote is typically y = 0 unless there is a vertical shift.

Front

Solve for x: 8^(2x) = 32

Back

Front

Solve for x: 8^(3x + 3) = 8^6

Back

x = 1.

Front

What is the general form of an exponential function?

Back

The general form is f(x) = a * b^(x - h) + k, where (h, k) is the translation of the graph.

Front

What does the base of an exponential function determine?

Back

The base determines the rate of growth or decay of the function.

Front

What is the effect of a positive vertical shift on an exponential graph?

Back

A positive vertical shift moves the graph upward, affecting the horizontal asymptote.