Graphing Exponentials

Front

What is the y-intercept of the graph y = 3^x + 4?

Back

(0, 5)

Front

Write the equation of the graph that has a y-intercept of 5 and passes through the point (0, 2).

Back

f(x) = 3^x + 2

Front

Does the equation y = 3^x + 4 represent an exponential function?

Back

Yes

Front

What is an exponential function?

Back

A function of the form f(x) = a*b^x where a is a constant, b is a positive real number, and b ≠ 1.

Front

What is the general shape of the graph of an exponential function?

Back

The graph increases rapidly for positive x and approaches the x-axis for negative x.

Front

What does the base of an exponential function determine?

Back

The base determines the rate of growth or decay of the function.

Front

If f(x) = 2^x, what is f(0)?

Back

f(0) = 1

Front

What happens to the graph of y = 3^x when you add a constant to it, like in y = 3^x + 4?

Back

The graph shifts vertically upwards by the constant added.

Front

What is the domain of an exponential function?

Back

The domain is all real numbers, (-∞, ∞).

Front

What is the range of the function y = 3^x + 4?

Back

The range is (4, ∞).