How many x-intercepts does the function f(x)=3(2x−1)(x+2)(8x−5)^2 have when graphed? (1 point)
The function f(x) has_ x-intercepts when graphed.
The function f(x) has 4 x-intercepts when graphed.
To find the x-intercepts of the function f(x), we need to set f(x) equal to zero and solve for x:
3(2x-1)(x+2)(8x-5)^2 = 0
Now, we can identify the number of x-intercepts by analyzing the factors separately:
1) (2x-1) = 0
Solving for x, we get:
2x = 1
x = 1/2
So, this factor contributes one x-intercept at x = 1/2.
2) (x+2) = 0
Solving for x, we get:
x = -2
This factor contributes one x-intercept at x = -2.
3) (8x-5)^2 = 0
To solve this, we take the square root of both sides:
8x-5 = 0
8x = 5
x = 5/8
So, this factor also contributes one x-intercept at x = 5/8.
Putting it all together, the function f(x) has a total of 3 x-intercepts when graphed.