Graphing Exponential Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a(b^x), where 'a' is a constant, 'b' is a positive real number, and 'x' is the exponent.

Front

What does the y-intercept of a function represent?

Back

The y-intercept of a function is the point where the graph of the function crosses the y-axis, which occurs when x = 0.

Front

How do you find the y-intercept of an exponential function?

Back

To find the y-intercept of an exponential function, substitute x = 0 into the function and solve for y.

Front

What is the general form of an increasing exponential function?

Back

An increasing exponential function has the form f(x) = a(b^x) where 'b' > 1.

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function is a horizontal line that the graph approaches as x approaches positive or negative infinity.

Front

For the function f(x) = 50(1.4^x), what is the y-intercept?

Back

The y-intercept is (0, 50), since f(0) = 50(1.4^0) = 50.

Front

What is the horizontal asymptote of the function f(x) = 13(0.5^(x-6))?

Back

The horizontal asymptote is y = 0.

Front

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

Back

The y-intercept is (0, 1), since 3^0 = 1.

Front

What is the effect of changing the base 'b' in an exponential function f(x) = a(b^x)?

Back

Changing the base 'b' affects the rate of growth or decay of the function; if b > 1, the function grows, and if 0 < b < 1, the function decays.

Front

What does it mean for an exponential function to be decreasing?

Back

An exponential function is decreasing if it has the form f(x) = a(b^x) where 0 < b < 1.