Exponential Functions Review 2024

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 does it mean for a function to reflect over the x-axis?

Back

Reflecting over the x-axis means that for every point (x, y) on the graph of the function, there is a corresponding point (x, -y). This changes the sign of the output values.

Front

What is the y-intercept of an exponential function?

Back

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

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote is a horizontal line that the graph of the function approaches as x approaches positive or negative infinity. For functions of the form f(x) = a * b^x + k, the horizontal asymptote is y = k.

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a fixed percentage over a period of time, represented by the function f(x) = a * b^x where b > 1.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a fixed percentage over a period of time, represented by the function f(x) = a * b^x where 0 < b < 1.

Front

How do you determine if a function is growing or decaying?

Back

If the base 'b' in the function f(x) = a * b^x is greater than 1, the function is growing. If 'b' is between 0 and 1, the function is decaying.

Front

What transformation occurs when you add a constant to an exponential function?

Back

Adding a constant 'k' to an exponential function f(x) = a * b^x results in a vertical shift. If k > 0, the graph shifts up; if k < 0, it shifts down.

Front

What transformation occurs when you add a value to the exponent in an exponential function?

Back

Adding a value 'c' to the exponent in f(x) = a * b^(x+c) results in a horizontal shift. If c > 0, the graph shifts left; if c < 0, it shifts right.

Front

What is the effect of a negative sign in front of an exponential function?

Back

A negative sign in front of an exponential function, such as f(x) = -a * b^x, reflects the graph over the x-axis.