Excel in math and science.

Join using Facebook Join using Google Join using email

Existing user? Log in

Your answer seems reasonable. Find out if you're right!

That seems reasonable. Find out if you're right!

Join using Facebook Join using Google Join using email

Existing user? Log in

Rational Functions

Rational Functions Warmup

What is the y-intercept of the graph of $y=\dfrac{(x+3)(x-8)}{(x-6)(x+2)}$

6 or -2 -3 or 8

-\dfrac{5}{4}

\dfrac{11}{8}

-2

Show explanation

by Brilliant Staff

$\dfrac{(2x+2)}{(x+2)(x+7)} = 1$ What are the possible values of $x$ ?

x=-3

x=-3

x=2

x=-3

x=-4

x=-4

x=2

x=-4

x=2

There are no values of

x

which satisfy this expression

Show explanation

by Brilliant Staff

What is the range of the function defined by $f(x) = \dfrac{(x+2)(x+2)(x+2)}{(x+2)} ?$

\mathbb{R}

[2,\infty)

[-2,\infty)

(0,\infty)

[0,\infty)

(-\infty,0]

(-\infty,0)

Show explanation

by Brilliant Staff

The red line above is a graph of $y=f(x).$ The graph travels through the points $(3,0)$ and $(0, -2.25).$

The blue line shows the horizontal asymptote of $f(x)$ .

What is a possible definition for $f(x)$ ?

f(x) = \dfrac{(x-3)}{(x+2)(x-2)(x-2)}

f(x) = \dfrac{(x-3)}{(x-2)(x-2)}

f(x) = \dfrac{(x-3)}{2(x+2)(x-2)}

f(x) = \dfrac{(x-3)(x-3)}{(x+2)(x-2)}

f(x) = \dfrac{(x-3)(x-2)}{(x+2)(x-2)}

f(x) = \dfrac{(x-3)(x+3)}{(x+2)(x-2)}

f(x) = \dfrac{(x-3)}{(x+2)(x-2)}

Show explanation

by Brilliant Staff

Where are the vertical asymptotes of the function $f(x) = \dfrac{(x-6)(x-4)}{2(x-4)(x+3)}$ ?

x=-3

x=-4

x=4

and

x=6

x=-3

and

x=4

x=-6

and

x=-4

This function has no vertical asymptotes

x=3

and

x=-4

Show explanation

by Brilliant Staff