What is the graph of the function f(x) = the quantity x squared minus 9x plus 20 over the quantity x minus 4?

QUESTION POSTED AT 01/06/2020 - 03:25 PM

Answered by admin AT 01/06/2020 - 03:25 PM

Answer:

Given : f(x) = the quantity x squared minus 9x plus 20 over the quantity x minus 4.

Then:

the quantity x squared minus 9x plus 20 means x^2-9x+20

over means divide

the quantity x minus 4 means x -4

then;  the function becomes

f(x) = \frac{x^2-9x+20}{x-4}                     .....[1]

Factorize:

x^2-9x+20 =  x^2-4x-5x+20 =x(x-4)-5(x-4) =(x-4)(x-5)

Then;

[1] ⇒ f(x) = \frac{(x-4)(x-5)}{x-4}

Now, divide denominator and numerator by x-4 we have;

f(x)=y= x-5                      ......[2]

Now, find x-intercepts and y-intercepts to graph the function:

x-intercepts are where the graph crosses the x-axis i.e,

substitute y = 0 in [2] to solve for x

0 =x-5

Add both sides by 5 we get;

0+5=x-5+5

Simplify:

x =5

X-intercepts = (5, 0)

y-intercepts are where the graph crosses the y-axis i,e

Substitute x = 0 in [2] and solve for y;

y = 0-5

y = -5

y-intercepts = (0, -5)

You can see the graph of the given function as shown below:



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