Exponential Graphs

Front

What is an exponential graph?

Back

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

Tags

CCSS.HSF-IF.C.7E

Front

What does exponential growth look like on a graph?

Back

Exponential growth appears as a curve that rises steeply to the right, indicating that as 'x' increases, 'y' increases rapidly.

Tags

CCSS.HSF-IF.C.7E

Front

What does exponential decay look like on a graph?

Back

Exponential decay appears as a curve that falls steeply to the right, indicating that as 'x' increases, 'y' decreases rapidly.

Tags

CCSS.HSF-IF.C.7E

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function is the point where the graph crosses the y-axis, which occurs at (0, a) where 'a' is the initial value.

Tags

CCSS.HSF-IF.C.7E

Front

What is a zero of a function?

Back

A zero of a function is a value of 'x' for which the function's output (y) is zero. It is the point where the graph intersects the x-axis.

Tags

CCSS.HSF-IF.C.7D

Front

How can you identify a linear graph?

Back

A linear graph can be identified by a straight line, indicating a constant rate of change between 'x' and 'y'.

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change and are represented by straight lines, while exponential functions have a variable rate of change and are represented by curves.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers (-∞, ∞), as 'x' can take any value.

Front

What is the range of an exponential function?

Back

The range of an exponential function is (0, ∞) for exponential growth and (-∞, 0) for exponential decay.

Tags

CCSS.HSF-IF.C.7E

Front

What is the base in an exponential function?

Back

The base in an exponential function is the constant 'b' in the equation y = a * b^x, which determines the rate of growth or decay.

Tags

CCSS.HSF-IF.C.8B