Exponential Parent Function Graph Math

Create a table of points.

Exponential parent function graph math. The parent graph of any exponential function crosses the y axis at 0 1 because anything raised to the 0 power is always 1. The graph of an exponential function a parent function. Scroll down the page for more examples and solutions. One that isn t shifted has an asymptote of y 0.

The following figures show the graphs of parent functions. Just as with other parent functions we can apply the four types of transformations shifts reflections stretches and compressions to the parent function latex f left x right b x latex without loss of shape. Draw a smooth curve through the points. Figure a for instance shows the graph of f x 2 x and figure b shows.

Transformations of exponential graphs behave similarly to those of other functions. Y 1 3 x. This is the parent function of exponential functions with base b. Then plot the points and sketch the graph.

Graph the following function. Given an exponential function of the form latex f left x right b x latex graph the function. The graphs of exponential decay functions can be transformed in the same manner as those of exponential growth. These parent functions illustrate that as long as the exponent is positive the graph of an exponential function whose base is greater than 1 increases as x increases an example of exponential growth whereas the graph of an exponential function whose base is between 0 and 1 decreases towards the x axis as x increases an example of exponential decay.

Notice that the graph gets close to the x axis but never touches it. Plot at least 3 point from the table including the y intercept latex left 0 1 right latex. Linear quadratic cubic absolute reciprocal exponential logarithmic square root sine cosine tangent. The domain of f x 2x f x 2 x is all real numbers the range is 0 0 and the horizontal asymptote is y 0 y 0.

The graph below displays the graphs of all of the functions. Make a table of values. The graph below shows the exponential growth function f x 2x f x 2 x. 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.

This function produces an exponential graph that slopes upward and becomes steeper as the value of x increases. Using the x and y values from this table you simply plot the coordinates to get the graphs. The most widely known exponential parent function involves euler s number e and follows the formula y e x. State the domain and range.

The basic parent function of any exponential function is f x bx where b is the base.