Quiz about Rational Functions

Question 1

Camila tried to reduce the following expression to lowest terms:

$$\frac{x^{2}-4 x+4}{x^{2}+4 x+4}$$

This is her work:

Factoring the numerator: $$x^{2}-4 {x}+4=({x}+2)({x}-2)$$

Factoring the denominator: $$x^{2}+4 {x}+4=(x+2)^{2}$$

Finding excluded values: $$x 
eq-2$$

Reducing to lowest terms:

$$\frac{x^{2}-4 x+4}{x^{2}+4 x+4}=\frac{(x+2)(x-2)}{(x+2)^{2}}=\frac{x-2}{x+2}$$

What mistake did Camila make?

Accepted Answer

Covalent bond

Answer

She didn't factorn the numerater corredly

Answer

She did not exclude $$x=0$$

Answer

She didn't exclude $$x=2$$ which makes the mumerator equal to zero

Answer

She excluded $$x=-2$$, which does not make the numerator in the new expression equal to zero.

Question 2

The equation shown is used to find the force of gravity, F, between two objects, where $$G$$ is the gravitational constant, $$m_1$$ and $$m_2$$ are the masses of the two objects, and $$r$$ is the distance between the two objects.

$${F}=\frac{G m_1 m_2}{r^{2}}$$

Which equation correctly shows the distance between the two objects?

Accepted Answer

Covalent bond

Answer

$${r}=\sqrt{\frac{G m_1 m_2}{F}}$$

Answer

$${r}=\sqrt{\frac{F}{G m_1 m_2}}$$

Answer

$$ {r}=\frac{\sqrt{G m_1 m_2}}{F} $$

Answer

$${r}=\frac{\sqrt{F}}{G m_1 m_2}$$

Question 3

In the expression $$p(x)=\frac{x+3}{x^{2}+2 x-3}$$, check if $$p$$ has a zero, a vertical asymptote, or a removable discontinuity at $$x=1$$.

Accepted Answer

Covalent bond

Answer

vertical asymptote

Answer

$$zeros$$

Answer

removable discontiunity

Answer

none of the above.

Question 4

In the expression $$p(x)=\frac{x^{2}+2 x-15}{x^{2}+10 x+25}$$, check if $$p$$ has a zero, a vertical asymptote, or a removable discontinuity at $${x}=-3$$.

Accepted Answer

Covalent bond

Answer

$$zero$$

Answer

removable dicontinunity

Answer

Vertical asympote

Answer

None of the above

Question 5

In the rational function $$f(x)=\frac{6 x^{3}-x^{2}+7}{2 x+5}$$, what is the pick value of $$f(x)$$ when $$x \rightarrow -\infty$$

Accepted Answer

Covalent bond

Answer

$$+\infty$$

Answer

$$-\infty$$

Answer

$$0$$

Answer

$$6$$

Rational Functions Precalculus Maths Problems and Solutions

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