Excel in math and science.

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Rational Functions

Rational Functions Warmup

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

-3 or 8 -2 2 6 or -2

\dfrac{11}{8}

-\dfrac{5}{4}

by Brilliant Staff

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

x=2

x=-3

x=-4

x=-3

x=2

x=-3

There are no values of

x

which satisfy this expression

x=2

x=-4

x=-4

by Brilliant Staff

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

[0,\infty)

(0,\infty)

[2,\infty)

(-\infty,0]

[-2,\infty)

\mathbb{R}

(-\infty,0)

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)(x-2)}{(x+2)(x-2)}

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

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=-6

and

x=-4

x=-3

and

x=4

x=3

and

x=-4

This function has no vertical asymptotes

x=4

and

x=6

x=-4

by Brilliant Staff