Exponential and Logarithmic Graphs

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is f(x) = a * b^x, where a > 0 and b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(x) = a * b^x, where a > 0 and 0 < b < 1.

Front

How do you convert an exponential equation to logarithmic form?

Back

To convert an exponential equation a^b = c to logarithmic form, use the formula log_a(c) = b.

Tags

CCSS.HSF.BF.B.5

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions and logarithmic functions are inverses of each other. If y = a^x, then x = log_a(y).

Tags

CCSS.HSF.BF.B.5

Front

What is the base of the natural logarithm?

Back

The base of the natural logarithm is e, approximately equal to 2.718.

Tags

CCSS.HSF.BF.B.5

Front

How do you express log_a(b) in terms of natural logarithms?

Back

log_a(b) can be expressed as ln(b) / ln(a) using the change of base formula.

Front

What does the graph of an exponential growth function look like?

Back

The graph of an exponential growth function rises rapidly as x increases, starting from a positive y-intercept.

Tags

CCSS.HSF-IF.C.7E

Front

What does the graph of an exponential decay function look like?

Back

The graph of an exponential decay function decreases rapidly as x increases, approaching the x-axis but never touching it.

Tags

CCSS.HSF-IF.C.7E

Front

What is the effect of a vertical translation on the graph of an exponential function?

Back

A vertical translation shifts the graph up or down without changing its shape.

Tags

CCSS.HSF-IF.C.7E

Front

How do you find the x-intercept of an exponential function?

Back

An exponential function does not have an x-intercept because it never touches the x-axis.

Tags

CCSS.HSF-IF.C.7E