Exponential Parent Graph Math

The basic parent function of any exponential function is f x bx where b is the base. The gradually steeper curve is produced because of the geometric progression that the function is following. While horizontal and vertical shifts involve adding constants to the input or to the function itself a stretch or compression occurs when we multiply the parent function f x bx f x b x by a constant a 0 a 0.

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When graphing an exponential function remember that the graph of an exponential function whose base number is greater than 1 always increases or rises as it moves to the right.

Exponential parent graph math. Just as with other parent functions we can apply the four types of transformations shifts reflections stretches and compressions to the parent function f x bx f x b x without loss of shape. One that isn t shifted has an asymptote of. The following table shows the transformation rules for functions. Each output value is the product of the previous output and the base 2.

For example if we begin by graphing the parent function f x 2x f x 2 x we can then graph the stretch using a 3 a 3 to get g x 3 2 x g x 3 2 x and the compression using a. Linear quadratic cubic absolute reciprocal exponential logarithmic square root sine cosine tangent. This function produces an exponential graph that slopes upward and becomes steeper as the value of x increases. Scroll down the page for more examples and solutions.

We call the base 2 the constant ratio in fact for any exponential function with the form latex f left x right a b x latex b is the constant ratio of the function this means that as the input increases by 1 the output value will be the product of the base and the previous output regardless of the value of a. When the base is greater than 1 a growth the graph increases and when the base is less than 1 a decay the graph decreases. Write the equation of an exponential function that has been transformed. For example f x 2 x is an exponential function as is.

But the domain and range are the same for both parent functions and both graphs have an asymptote of. The most widely known exponential parent function involves euler s number e and follows the formula y e x. This video is unavailable. Graphs of functions the following figures show the graphs of parent functions.

Transformations of exponential graphs behave similarly to those of other functions. As the graph moves to the left it always approaches 0 but never actually get there. Figure a for instance shows the graph of f x 2 x and figure b shows using the x and y values from this table you simply plot the coordinates to get the graphs. The graph of an exponential function a parent function.