Question

Describe the behavior of the graph at the x-intercepts for the functions f(x)=(2x-7)^7 (x+3)^4. Be sure to identify each x-intercept and justify your answer.

Answer 1

Answer:

Touches at -3 and crosses at 3.5

Step-by-step explanation:

f(x)=(2x-7)^7 (x+3)^4 is given

To find x intercepts:

for x intercepts the value of f(x) =0

Hence f(x)=(2x-7)^7 (x+3)^4=0

Solving we get

2x-7 =0 or x+3 =0

x = 3.5 or x=-3

Thus we find the zeroes of the polynomial of f(x) are 3.5 and -3.

3.5 has a multiplicity of 7 and -3 a multiplicity of 4

Since 7 is odd, i.e. 3.5 has a multiplicity of odd number, hence f(x) crosses x axis at x 3.5

Since -3 has a multiplicity of an even number 4, we find that the curve touches x axis at the point -3.