Graphing Exponential Functions

Front

What is the y-intercept of the function y=3^x?

Back

(0, 1)

Front

Which function represents an increasing exponential function with a y-intercept of 50?

Back

y = 50(1.4)^x

Front

What is the general form of an exponential function?

Back

y = ab^x, where a is the initial value and b is the base.

Front

What does it mean for a function to exhibit exponential growth?

Back

The base b is greater than 1.

Front

What does it mean for a function to exhibit exponential decay?

Back

The base b is greater than 0 but less than 1.

Front

Determine if the function f(x) = (1/4)^x represents growth or decay.

Back

Decay

Front

What is the y-intercept of an exponential function?

Back

The point where the graph intersects the y-axis, found by evaluating f(0).

Front

How do you find the y-intercept of the function y = 50(1.4)^x?

Back

Evaluate f(0): y = 50(1.4)^0 = 50.

Front

What is the effect of changing the base in an exponential function?

Back

A larger base results in faster growth; a smaller base (greater than 0) results in slower growth or decay.

Front

What is the graph of an exponential function with a base greater than 1?

Back

It rises steeply as x increases.