Algebra 2 Unit 6 Day 1: Key features of 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 the base (a positive real number), and 'x' is the exponent.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function is the value of the function when x = 0, which is equal to 'a' in the function f(x) = a(b)^x.

Front

How do you identify the growth or decay of an exponential function?

Back

If the base 'b' is greater than 1, the function represents exponential growth. If 'b' is between 0 and 1, it represents exponential decay.

Front

What is the general form of an exponential growth function?

Back

The general form is f(x) = a(b)^x, where 'b' > 1.

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a(b)^x, where 0 < b < 1.

Front

What does the base of an exponential function represent?

Back

The base of an exponential function determines the rate of growth or decay. A larger base results in faster growth, while a smaller base (but greater than 0) results in slower growth or decay.

Front

What is the range of an exponential function?

Back

The range of an exponential function is all real numbers greater than 0 if the function is of the form f(x) = a(b)^x with a > 0.

Front

How do you find the y-intercept of the function f(x) = 10(5)^x?

Back

To find the y-intercept, substitute x = 0: f(0) = 10(5)^0 = 10.

Front

What is the decay rate in the function f(x) = 6.5(0.85)^x?

Back

The decay rate is 15%, as the base 0.85 indicates a decrease of 15% from the previous value.

Front

What does it mean if an exponential function has a y-intercept of 3?

Back

It means that when x = 0, the value of the function is 3, indicating the starting point of the graph.