Graphing Exponential Functions QUICK

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 is the general form of an increasing exponential function?

Back

The general form of an increasing exponential function is f(x) = a(b)^x, where 'a' > 0 and 'b' > 1.

Front

What is the general form of a decreasing exponential function?

Back

The general form of a decreasing exponential function is f(x) = a(b)^x, where 'a' > 0 and 0 < b < 1.

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function is typically y = 0.

Front

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

Back

The y-intercept of an exponential function f(x) = a(b)^x is found by evaluating f(0), which equals 'a'.

Front

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

Back

Exponential growth occurs when the base 'b' of the function f(x) = a(b)^x is greater than 1, resulting in the function increasing rapidly as 'x' increases.

Front

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

Back

Exponential decay occurs when the base 'b' of the function f(x) = a(b)^x is between 0 and 1, resulting in the function decreasing rapidly as 'x' increases.

Front

What is the significance of the base 'b' in an exponential function?

Back

The base 'b' determines 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 is the y-intercept of the function y = 50(1.4)^x?

Back

The y-intercept is 50, which is the value of the function when x = 0.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth increases as x increases (b > 1), while exponential decay decreases as x increases (0 < b < 1).