If f(x) = (x-4) (x+3) , determine the x-intercept of each function
a)y=f(x) b) y=-2f(x) c) y=(-(x+1))
thanks for the help !!!!!!
To find the x-intercept of a function, we need to set y equal to zero and solve for x. The x-intercept is the value of x at which the function crosses or intersects the x-axis.
a) For y = f(x) = (x-4)(x+3), we set y equal to zero: 0 = (x-4)(x+3). Since a product of factors is zero only if at least one of the factors is zero, we can set each factor equal to zero and solve for x.
Setting x-4 = 0, we find x = 4.
Setting x+3 = 0, we find x = -3.
So, the x-intercepts are x = 4 and x = -3.
b) For y = -2f(x), we substitute y with -2f(x) in the original function: 0 = -2(x-4)(x+3). We follow the same steps as in part a to find the x-intercepts.
Setting x-4 = 0, we find x = 4.
Setting x+3 = 0, we find x = -3.
So, the x-intercepts of -2f(x) are x = 4 and x = -3.
c) For y = (-(x+1)), we set y equal to zero: 0 = (-(x+1)). We can solve for x by multiplying both sides by -1 to get rid of the negative sign.
0 = x+1.
Subtracting 1 from both sides, we find x = -1.
So, the x-intercept of y = (-(x+1)) is x = -1.