Question

Plot points between and beyond each x-intercept and vertical asymptote. Find the value of the function at the given value of x.-537X15xf(x)=x-5(Simplify your answer. Type an integer or a simplified fraction.)

Answer 1

Given

$f(x)=\frac{5x}{x-5}$

Find

the values of function at given value of x

Explanation

at x = -5

substitute the value of x in given function

$\begin{gathered} f(-5)=\frac{5(-5)}{-5-5} \\ \\ f(-5)=-\frac{25}{(-10)} \\ \\ f(-5)=\frac{5}{2} \end{gathered}$

at x = -1

$\begin{gathered} f(-1)=\frac{5(-1)}{-1-5} \\ \\ f(-1)=-\frac{5}{(-6)} \\ \\ f(-1)=\frac{5}{6} \end{gathered}$

at x = 3

$\begin{gathered} f(3)=\frac{5(3)}{3-5} \\ \\ f(3)=\frac{15}{(-2)} \\ \\ f(3)=-\frac{15}{2} \end{gathered}$

at x = 1

$\begin{gathered} f(1)=\frac{5(1)}{1-5} \\ \\ f(1)=\frac{5}{(-4)} \\ \\ f(1)=-\frac{5}{4} \end{gathered}$

at x = 7

$\begin{gathered} f(7)=\frac{5(7)}{7-5} \\ \\ f(7)=\frac{35}{2} \\ \end{gathered}$

Final Answer

Therefore

at x = -5 , then function is 5/2

at x = -1 , then function is 5/6

at x = 1 , then function is -5/4

at x = 3 , then function is -15/2

at x = 7 , then function is 35/2