Answer:
The vertical intercepts is
(4/3,0) (3,0) (1,0)
The horinzontial intercepts is
(0,72)
The end behavior is
as x approaches positive infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches negative infinity.
Step-by-step explanation:
The vertical or y intercepts will be zeroes of the following factors.
[tex]3x + 4 = 0[/tex]
[tex]x - 1 = 0[/tex]
[tex](x - 3) {}^{2} = 0[/tex]
We solve for x each time.
[tex]x = - \frac{4}{3} [/tex]
[tex] x = 1[/tex]
[tex]x = 3[/tex]
Part B). We need to find the intercepts by setting the equation equal to zero.
The constant expanded will equal 72.
If x=0,
[tex] {0}^{y} = 0[/tex]
where y is any real number.
So this means all the exponets will equal 0. The constant will just add to the term. so our horinzontal intercept is
[tex]0 + 72 = 72[/tex]
Part C) End Behavior
The leading degree is even. Even Degree Polynomials like Quadratics tend to go approach positive infinity vertically as x approaches positive infinity, and as x approaches negative infinity, it approaches positive infinity vertically.
Our leading coefficient is negative so this means our quadratic will get reflected across the x axis.
Now this means, as x approaches positive infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches negative infinity.
