to graph the original function y=1/2x−4 and the vertically dilated function with a factor k=6. Determine the x-intercepts of both functions.
To graph the original function y=1/2x−4, we can start by finding the x-intercept. The x-intercept occurs when y=0, so we can set the equation equal to zero:
0 = 1/2x - 4
To solve for x, we can add 4 to both sides:
4 = 1/2x
Then, multiply both sides by 2:
8 = x
So the x-intercept of the original function is x = 8.
To graph the vertically dilated function with a factor of k = 6, we need to multiply the original function by 6:
y = 6(1/2x - 4)
Simplifying, we get:
y = 3x - 24
To find the x-intercept, we can set y equal to zero:
0 = 3x - 24
Adding 24 to both sides:
24 = 3x
Dividing both sides by 3:
8 = x
So the x-intercept of the dilated function is x = 8.
Thus, both functions have the x-intercept at x = 8.