How do i find the x and y intercept of y=5(3^x)
The X intercept is the point at which Y = 0. Since there is no way (that I know of at least) to make 3^X equal to 0, there is no X intercept.
The Y intercept is the point at which X is equal to 0. This is much easier to calculate, as you can just plug in 0 for x into the equation. 3^1 = 1, times 5 is 5. So the Y intercept is at (0,5).
x -6 -4 -2 0 2 4 6
y -36 -26 -16 -6 4 14 24
To find the x-intercept (where the graph of the equation crosses the x-axis), we set y equal to zero and solve for x.
Let's start with the equation y = 5(3^x).
Setting y = 0, we have 0 = 5(3^x).
Now, divide both sides of the equation by 5 to isolate the exponential term:
0/5 = (3^x).
Since any nonzero number raised to the power of 0 is 1, we get:
0 = 1.
This equation is not possible, meaning there are no x-intercepts for the given equation y = 5(3^x). Therefore, this exponential function does not cross the x-axis.
Moving on to finding the y-intercept (where the graph of the equation crosses the y-axis), we set x equal to zero and solve for y.
Plug in x = 0 into the equation y = 5(3^x):
y = 5(3^0).
Since any number raised to the power of 0 is 1, we have:
y = 5(1).
Finally, simplifying the expression gives:
y = 5.
Thus, the y-intercept of the equation y = 5(3^x) is (0, 5).