Answer:
6. an odd-degree polynomial function.
f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞
7. Length =x+10=8+10=18 inches
Width=x=8 inches
Step by step explanation;
6. The graph represent an odd-degree polynomial function.
The graph enters the graphing box from the bottom and goes up leaving through the top of the graphing box.This is a positive polynomial whose limiting behavior is given by;
f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞
7.
The area of a rectangle is given by l×w, where l is length and w is the width
Let=w=x , l=x+10 and A=144 in² then;
l×w=144
(x+10) × x = 144
x²+10x =144......................complete squares on both sides
x²+10x+25=144+25
x²+10x+25=144+25................factorize
(x+5)²=169.......................square root the right-hand side
x+5= ±√169
x+5=±13.
x+5=13⇒⇒⇒x=8
x+5=-13⇒⇒⇒x= --18
x=8 inches....................value of width should be positive
Length =x+10=8+10=18 inches
Width=x=8 inches
Answer:
6. Since, by given graph,
The end behavior of the function f(x),
[tex]f(x)\rightarrow -\infty\text{ if }x\rightarrow -\infty[/tex]
[tex]f(x)\rightarrow +\infty\text{ if }x\rightarrow +\infty[/tex]
Thus, the function f(x) must has odd number of roots ( where the graph of a function intersects the x-axis )
⇒ The function must has odd number of solutions,
Again by the graph,
Graph of the function intersects the x-axis 5 times ( it touches the origin so it have the repeated root of x = 0 ),
Hence, the total number of real solution of f(x) is 5.
7. Let x represents the width of the rectangle( in inches ),
Given,
The length is 10 inches longer than the width,
⇒ Length of the rectangle = ( x + 10 ) inches
Thus, the area of the rectangle,
A = length × width = x(x+10)
According to the question,
A = 144 in²
⇒ x(x+ 10) = 144
[tex]x^2+10x=144[/tex]
[tex]x^2+10x-144=0[/tex]
[tex]x^2+18x-8x-144=0[/tex] ( Middle term splitting )
[tex]x(x+18)-8(x+18)=0[/tex]
[tex](x+18)(x-8)=0[/tex]
⇒ x = -18 or x = 8 ( By zero test property )
The width can not be negative,
Hence, the width of the rectangle would be 8 inches.
