Unit 8 Test

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent. The graph of an exponential function shows rapid growth or decay.

Front

How does the transformation y = a * f(x - h) + k affect the graph of f(x)?

Back

The transformation y = a * f(x - h) + k stretches or compresses the graph vertically by a factor of |a|, shifts it horizontally to the right by h units (if h > 0) or to the left (if h < 0), and shifts it vertically up by k units (if k > 0) or down (if k < 0).

Front

What does a vertical stretch by a factor of 2 mean for the function y = f(x)?

Back

A vertical stretch by a factor of 2 means that for every point on the graph of y = f(x), the y-coordinate is multiplied by 2, making the graph taller.

Front

What does a horizontal shift to the right by 3 units mean for the function y = f(x)?

Back

A horizontal shift to the right by 3 units means that the entire graph of y = f(x) is moved 3 units to the right along the x-axis.

Front

What is the effect of a vertical shift up by 1 unit on the function y = f(x)?

Back

A vertical shift up by 1 unit means that every point on the graph of y = f(x) is moved up 1 unit, resulting in the new function y = f(x) + 1.

Front

What is the parent function of exponential functions?

Back

The parent function of exponential functions is y = b^x, where b is a positive constant. This function serves as the basic form from which other exponential functions are derived.

Front

What does it mean for a function to be reflected over the x-axis?

Back

A reflection over the x-axis means that for every point (x, y) on the graph of the function, the new point will be (x, -y). This inverts the graph vertically.

Front

What is the transformation represented by the equation y = -3(1/4)^(x-2) + 2?

Back

This equation represents a vertical stretch by a factor of 3, a reflection over the x-axis, a horizontal shift to the right by 2 units, and a vertical shift up by 2 units.

Front

How do you identify an exponential growth function?

Back

An exponential growth function has a base greater than 1 in the form y = a * b^x, where a > 0 and b > 1. The graph rises steeply as x increases.

Front

What does it mean for a function to decay?

Back

A function is said to decay if it decreases as x increases. In exponential functions, this occurs when the base is between 0 and 1 (0 < b < 1).