Quiz about Rational Functions

Question 1

Aoi tried to reduce the following expression to lowest terms:

$$\frac{3 x+3}{x^{2}-1}$$

This is her work:

Factoring the numerator: $$3 {x}+3=3({x}+1)$$

Factoring the denominator: $$x^{2}-1=({x}+1)({x}-1)$$

Finding excluded values: : $$x 
eq 0$$ and $$x 
eq \pm 3$$

Reducing to lowest terms:

$$\frac{3 x+3}{x^{2}-1}=\frac{3(x+1)}{(x+1)(x-1)}=\frac{3}{x+1}$$

What mistake did Aoi make?

Accepted Answer

Covalent bond

Answer

She excluded $$x=0$$, which doesnot make the denominator equal to 0 .

Answer

She excluded $$x=1$$, which doesnot make the numerator equal to zero.

Answer

She excluded $$x=-1$$ whick doesnot make, the new expression equal to 20 .

Answer

She did not factor the denominator correctly.

Question 2

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 3

Raiden tried to reduce the following expression to lowest terms:

$$\frac{4 x^{2}-12 x}{3 x^{2}+15 x}$$

This is his work:

Factoring the numerator: $$4 x^{2}-12 {x}=4 {x}({x}-3)$$

Factoring the denominator: $$3 x^{2}+15 x=3 x(x+5)$$

Reducing to lowest terms:

$$\frac{4 x^{2}-12 x}{3 x^{2}+15 x}=\frac{4 x(x-3)}{3 x(x+5)}=\frac{4(x-3)}{3(x+5)}$$

Finding excluded values: $$x 
eq-5$$

What mistake did Raiden make?

Accepted Answer

Covalent bond

Answer

He didn't exper ex ilude $$x>0$$, which mates
the denominator in the original expressionequal
to zero.

Answer

He didn't exclude $$x, 23$$ which makes the numerator equal to zero.

Answer

He didn't factor the numerator correalty

Answer

He excluded $$x=-5$$ which does not make the numerator equal to zero.

Question 4

What values of $${x}$$ must be excluded from the domains of the simplified version of the expression $$\frac{2 x+14}{x^{2}+6 x-7}$$

Accepted Answer

Covalent bond

Answer

$$x=-7 	ext{ and }$$x=1$$

Answer

$$x=7 	ext { and } $$x=-1$$

Answer

$$x=-7 	ext { and } x=-1$$

Answer

$$x=7 	ext { and }$$x=1$$

Question 5

What values of $${x}$$ must be excluded from the domains of the simplified version of the expression $$\frac{x^{2}-64}{x^{2}+16 x+64}$$

Accepted Answer

Covalent bond

Answer

$$x=-8$$

Answer

$$x=8$$

Answer

$$x=16$$

Answer

$$x=0$$

Rational Functions Precalculus Maths Problems and Solutions

Many students find Rational Functions for Precalculus particularly challenging. Strengthen your concepts and gain confidence for your exams by solving free questions for Rational Functions from for Precalculus preparation.