if f(x)= (x-4)(x=3) determine the x intercept of the funtion if
y= -2f(x)...
i just don't know if the -2 affects the answer because that only affects the y co ordinates. in the book it says 4,-3 but i don't know why.
if this is true if the they were asking me to find the y interpct of the function what do i do. THANKS!!!!
To find the x-intercept of the function f(x) = (x - 4)(x - 3), you need to set the function equal to zero and solve for x.
1. Start with f(x) = (x - 4)(x - 3) and set it equal to zero: (x - 4)(x - 3) = 0.
2. Now, you can use the zero-product property, which states that if a product of factors equals zero, then at least one of the factors must be zero.
3. So, set each factor equal to zero and solve for x:
x - 4 = 0 or x - 3 = 0.
Solving the first equation: x - 4 = 0
Add 4 to both sides: x = 4.
Solve the second equation: x - 3 = 0
Add 3 to both sides: x = 3.
4. Therefore, the x-intercepts of the function f(x) = (x - 4)(x - 3) are x = 4 and x = 3.
Now, let's consider the function y = -2f(x).
Since the -2 is multiplying the entire f(x), it affects the y-intercept but not the x-intercepts. The x-intercepts are determined by where the function f(x) crosses the x-axis, and they remain the same regardless of any constant factor such as -2 in front of f(x).
So, the x-intercepts of y = -2f(x) will still be x = 4 and x = 3.
If you were asked to find the y-intercept of the function y = -2f(x), you would need to evaluate the function when x = 0, as the y-intercept occurs when x = 0. However, without knowing the specific form of f(x), we cannot determine the y-intercept in this case.