Help please
State the x and y-intercepts for each function.
f(x)= -x^3+4x
y-intercept is where x=0: f(0) = 0
x-intercept is where y=0
y = x(4-x^2)
= x(2-x)(2+x)
So, the x-intercepts are at -2,0,+2
thanks for the help
To find the x-intercepts of a function, set the function equal to zero and solve for x.
For f(x) = -x^3 + 4x, set the function equal to zero:
0 = -x^3 + 4x
Now, we need to solve this equation for x. There are a few ways to solve a cubic equation like this, but one common approach is to factor out an x:
0 = x (-x^2 + 4)
Setting each factor equal to zero:
x = 0 or -x^2 + 4 = 0
The first factor gives us x = 0, so one x-intercept is (0, 0).
Now let's solve the second equation for x:
-x^2 + 4 = 0
Adding x^2 to both sides:
x^2 = 4
Taking the square root of both sides:
x = ±2
This gives us two additional x-intercepts: (-2, 0) and (2, 0).
To find the y-intercept, simply substitute x = 0 into the equation of the function:
f(0) = -0^3 + 4(0)
f(0) = 0
So, the y-intercept is (0, 0).
In summary, the x-intercepts are (0, 0), (-2, 0), and (2, 0), and the y-intercept is (0, 0) for the function f(x) = -x^3 + 4x.