Transforming Exponential and Log Functions

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 a positive real number, and x is the variable. It shows rapid growth or decay.

Front

What is a logarithmic function?

Back

A logarithmic function is the inverse of an exponential function, expressed as y = log_b(x), where b is the base and x is the argument. It answers the question: 'To what exponent must b be raised to produce x?'

Front

What is the parent function of exponential functions?

Back

The parent function of exponential functions is y = b^x, where b > 0 and b ≠ 1.

Tags

CCSS.HSF-IF.C.7E

Front

What is the parent function of logarithmic functions?

Back

The parent function of logarithmic functions is y = log_b(x), where b > 0 and b ≠ 1.

Tags

CCSS.HSF-IF.C.7E

Front

What happens to the graph of y = b^x when b > 1?

Back

The graph of y = b^x is increasing and shows exponential growth.

Tags

CCSS.HSF-IF.C.7E

Front

What happens to the graph of y = b^x when 0 < b < 1?

Back

The graph of y = b^x is decreasing and shows exponential decay.

Tags

CCSS.HSF-IF.C.7E

Front

How does the graph of y = log_b(x) behave?

Back

The graph of y = log_b(x) is increasing, passes through the point (1,0), and approaches the y-axis (x=0) but never touches it.

Tags

CCSS.HSF-IF.C.7E

Front

What is a horizontal shift in graph transformations?

Back

A horizontal shift moves the graph left or right. For example, y = b^(x + c) shifts the graph left by c units.

Tags

CCSS.HSF.BF.B.3

Front

What is a vertical shift in graph transformations?

Back

A vertical shift moves the graph up or down. For example, y = b^x + k shifts the graph up by k units.

Tags

CCSS.HSF.BF.B.3

Front

What does the equation y = log_b(x + c) represent?

Back

It represents a horizontal shift of the logarithmic graph to the left by c units.

Tags

CCSS.HSF-IF.C.7E