Question

Which parent functions have an intercept at (0,0)Choose all that are correct.
Linear
Quadratic
Radical
Absolute Value
Rational
Exponential
Logarithmic (Log)
Cubic
Cube Root

Answer 1

Answer:

Linear, Quadratic, Radical, Absolute Value, Cubic, Cube Root

Step-by-step explanation:

To find:

Which functions have an intercept at (0, 0).

That means, when we put a value $x=0$ in the $y =f(x)$, value of $y=0$.

Let us discuss each parent function one by one:

1. Linear:

$y = x$

When we put x = 0, y = 0

Therefore, it has intercept at (0, 0).

2. Quadratic:

$y = x^2$

When we put x = 0, y = 0

Therefore, it has intercept at (0, 0).

3. Radical:

$y = \sqrt x$

When we put x = 0, y = 0

Therefore, it has intercept at (0, 0).

4. Absolute Value:

$y = |x|$

When we put x = 0, y = 0

Therefore, it has intercept at (0, 0).

5. Rational:

$y = \dfrac{1}{x}$

When we put $x = 0\Rightarrow y \rightarrow \infty$

Therefore, it does not have intercept at (0, 0).

6. Exponential:

$y = b^x$

b is any base

When we put $x = 0\Rightarrow y =1$

Therefore, it does not have intercept at (0, 0).

7. Logarithmic:

$y = logx$

When we put $x = 0 \Rightarrow y\rightarrow$ Not defined

Therefore, it does not have intercept at (0, 0).

8. Cubic:

$y = x^3$

When we put $x = 0\Rightarrow y =0$

Therefore, it has intercept at (0, 0).

9. Cube Root:

$y = \sqrt[3]x$

When we put $x = 0\Rightarrow y =0$

Therefore, it has intercept at (0, 0).

Answer 2

Question:

Consider the cube root parent function.

( graph in photo below )

Complete the statements to make them true.

A cube root function will ( 1 ) ________ have an x-intercept and ( 2 ) ________ have a y-intercept.

For the parent cube root function, ( 3 ) ____________ located at .

Answer:

1. always

2. always

3. both intercepts are

Explanation:

( In photo below )