Transformations of Logarithmic & Exponential Functions

Front

What is a logarithmic function?

Back

A logarithmic function is the inverse of an exponential function, typically expressed in the form y = log_b(x), where b is the base.

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, and x is the exponent.

Front

What does it mean to reflect a function over the x-axis?

Back

Reflecting a function over the x-axis means to invert the output values, changing the sign of the function's values.

Tags

CCSS.HSF.BF.B.3

Front

What is a vertical stretch in the context of transformations?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

Front

How does adding a constant to a function affect its graph?

Back

Adding a constant to a function results in a vertical shift of the graph; if the constant is positive, the graph shifts up, and if negative, it shifts down.

Front

What is the effect of multiplying a function by a fraction between 0 and 1?

Back

Multiplying a function by a fraction between 0 and 1 results in a vertical shrink of the graph.

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases at a rate proportional to its current value, typically represented by functions of the form y = a(b^x) where b > 1.

Tags

CCSS.HSF-LE.A.1A

Front

What is the parent function of an exponential function?

Back

The parent function of an exponential function is y = b^x, where b is a positive constant.

Front

What is the parent function of a logarithmic function?

Back

The parent function of a logarithmic function is y = log_b(x), where b is a positive constant.

Tags

CCSS.HSF-IF.C.7E

Front

How does a negative coefficient affect the graph of an exponential function?

Back

A negative coefficient reflects the graph of the exponential function over the x-axis.

Tags

CCSS.HSF-IF.C.7E