The x-intercept is the point of intersection of the function with the x-axis. Similarly, the y-intercept is the point of intersection with the y-axis.
x-intercept: Does not exist y-intercept: (0,88)
Practice makes perfect
We want to find the x- and y-intercepts of the given function. Let's begin with the x-intercept.
Finding the x-intercept
Think of the point where the graph of an equation crosses the x-axis. This is the x-intercept. The y-value of that ( x, y) coordinate pair is 0, so to find the x-intercept of the equation we should substitute 0 for y and solve for x.
Notice that now we want to find the power to which 3 must be raised in order to get - 781. Raising a positive number to any power always results in a positive number. Since the left-hand side is negative, there are no values of x that satisfy this equation. Therefore, there are no x -intercepts.
Finding the y-intercept
Let's use the same concept to find the y-intercept. Consider the point where the graph of the equation crosses the y-axis. The x-value of the ( x, y) coordinate pair at the y-intercept is 0. Therefore, substituting 0 for x will give us the y-intercept.
