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 the base (a positive real number), and 'x' is the exponent.

Front

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

Back

The graph of an exponential function increases rapidly for positive values of x and approaches the x-axis (y=0) but never touches it for negative values of x.

Front

What is the horizontal asymptote of an exponential function?

Back

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

Front

What does the base 'b' in an exponential function determine?

Back

The base 'b' determines the rate of growth or decay of the function. If b > 1, the function grows; if 0 < b < 1, the function decays.

Front

How does changing the value of 'a' affect the graph of an exponential function?

Back

Changing the value of 'a' affects the vertical stretch or compression of the graph. If 'a' is positive, the graph is above the x-axis; if 'a' is negative, the graph is reflected across the x-axis.

Front

What is the equation of the asymptote for the function f(x) = a * b^x?

Back

The equation of the asymptote is y = 0.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, (-∞, ∞).

Front

What is the range of an exponential function?

Back

The range of an exponential function is all positive real numbers, (0, ∞).

Front

How do you find 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 is the significance of the x-intercept in an exponential function?

Back

An exponential function has no x-intercept if 'a' is positive, as it never crosses the x-axis. If 'a' is negative, it will cross the x-axis at one point.