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 !!!!!!
(a)
The x-intercept would be the zeroes of the function, that is the values of x such that:
f(x) = (x-4) (x+3) = 0
For this to happen, (x-4)=0 or (x+3)=0 giving x=4 or x=-3.
(b)
Multiplying f(x) by -2 does not change the values of the zeroes.
(c)
Equate the function expression to zero and solve for x, i.e. the value of x which makes the function (expression) = 0.
a) To find the x-intercepts of f(x), set y = 0:
0 = (x - 4)(x + 3)
Now, we can use the zero-product property to solve for x:
x - 4 = 0 or x + 3 = 0
Simplifying, we find:
x = 4 or x = -3
Therefore, the x-intercepts of f(x) are x = 4 and x = -3.
b) To find the x-intercepts of -2f(x), set y = 0:
0 = -2[(x - 4)(x + 3)]
Now, let's use the zero-product property again:
(x - 4)(x + 3) = 0
Expanding and simplifying, we get:
x^2 - x - 12 = 0
We can factor this quadratic equation as:
(x - 4)(x + 3) = 0
Using the zero-product property once more:
x - 4 = 0 or x + 3 = 0
That implies:
x = 4 or x = -3
Therefore, the x-intercepts of -2f(x) are x = 4 and x = -3 as well.
c) To find the x-intercepts of -(x + 1), set y = 0:
0 = - (x + 1)
Multiplying both sides by -1, we find:
0 = x + 1
Subtracting 1 from both sides, we have:
-1 = x
So, the x-intercept of y = -(x + 1) is x = -1.
You're welcome! If these answers don't make you crack a smile, I'll clown around some more!
To determine the x-intercept of a function, we set the y-value (or f(x)) to 0 and solve for x.
a) For y = f(x) = (x - 4)(x + 3):
Setting y = 0, we have:
(x - 4)(x + 3) = 0
Now, we can apply the zero product property: if a * b = 0, then a = 0 or b = 0.
Setting each factor to 0:
x - 4 = 0 or x + 3 = 0
Solving for x, we find:
x = 4 or x = -3
Therefore, the x-intercepts are x = 4 and x = -3.
b) For y = -2f(x) = -2(x - 4)(x + 3):
Setting y = 0, we have:
-2(x - 4)(x + 3) = 0
Again, we apply the zero product property:
-2(x - 4) = 0 or (x + 3) = 0
Simplifying and solving for x:
x - 4 = 0 or x = -3
Adding 4 to both sides of the first equation gives:
x = 4
Therefore, the x-intercepts are x = 4 and x = -3.
c) For y = -(x + 1):
Setting y = 0, we have:
-(x + 1) = 0
Multiplying both sides by -1:
x + 1 = 0
Subtracting 1 from both sides:
x = -1
Therefore, the x-intercept is x = -1.
The x-intercepts for the given functions are:
a) x = 4, x = -3
b) x = 4, x = -3
c) x = -1
To find the x-intercept of a function, we need to find the value(s) of x where the function crosses the x-axis. At the x-intercept, the value of y is equal to zero.
a) y = f(x) = (x-4)(x+3)
To find the x-intercept of y = f(x), set y = 0 and solve for x:
0 = (x-4)(x+3)
Apply the zero product property. Since the product is zero, one or both factors must be zero:
x - 4 = 0 or x + 3 = 0
Solve each equation separately:
x - 4 = 0 -> x = 4
x + 3 = 0 -> x = -3
Therefore, the x-intercepts of function y = f(x) are x = 4 and x = -3.
b) y = -2f(x) = -2(x-4)(x+3)
To find the x-intercept of y = -2f(x), set y = 0 and solve for x:
0 = -2(x-4)(x+3)
Divide both sides of the equation by -2 to simplify:
0 = (x-4)(x+3)
Using the zero product property again:
x - 4 = 0 or x + 3 = 0
Solve each equation separately:
x - 4 = 0 -> x = 4
x + 3 = 0 -> x = -3
Therefore, the x-intercepts of function y = -2f(x) are also x = 4 and x = -3.
c) y = (-(x+1))
To find the x-intercept of y = (-(x+1)), set y = 0 and solve for x:
0 = -(x+1)
Divide both sides of the equation by -1 to isolate x:
0 = x + 1
Subtract 1 from both sides:
-1 = x
Therefore, the x-intercept of function y = (-(x+1)) is x = -1.
So, the x-intercept for each function is:
a) x = 4 and x = -3
b) x = 4 and x = -3
c) x = -1