Question

What is the graph of the function f(x) = the quantity of x plus 7, all over x minus 4?

Answer 1

Let’s sketch the graph of f(x) = $\frac{x+7}{x-4}$

First, since this is a rational function we are going to have to be careful with division by zero issues. So, we can see from this equation that we’ll have to avoid since that will give division by zero.

Now, let’s just plug in some values of x and see what we get. Make x-y table first

x y

-20 0.542

-10 0.214

-7 0 (x intercept )

0 -1.75 (y-intercept)

3 -10

5 12

10 2.833

20 1.688

Now find the horizontal and vertical asymptotes

Vertical asymptote: Find the vertical asymptotes by setting the denominator equal to zero and solving.

Put denominator = 0

x-4 = 0

x=4

Horizontal Asymptote:

y = leading coefficient of x (in numberator )/leading coefficient of x (in denominator)

y = 1

Here is a sketch of this graph.

Answer 2

Reciprocal function..... .