Question

All Parent functions have both x- intercepts and y-intercepts EXCEPT. I. Linear II. Absolute Value III.Quadratic IV. Cubic V.Square root VI. Cube root VII. Reciprocal VIII. Exponential IX. Logarithmic

Answer 1

Answer:

Reciprocal, Exponential and Logarithmic.

Step-by-step explanation:

x intercept is the value of x where y value is 0.

y intercept is the value of y where x value is 0.

Let us have a look at the possibility for each parent function as given.

I. Linear

$y =x$

When x = 0, y = 0 and

When y = 0, x = 0

Therefore, both x and y intercept exist.

II. Absolute value

$y =|x|$

When x = 0, y = 0 and

When y = 0, x = 0

Therefore, both x and y intercept exist.

III. Quadratic

$y =x^{2}$

When x = 0, y = 0 and

When y = 0, x = 0

Therefore, both x and y intercept exist.

IV. Cubic

$y =x^3$

When x = 0, y = 0 and

When y = 0, x = 0

Therefore, both x and y intercept exist.

V. Square root

$y =\sqrt x$

When x = 0, y = 0 and

When y = 0, x = 0

Therefore, both x and y intercept exist.

VI. Cube root

$y =\sqrt[3]x$

When x = 0, y = 0 and

When y = 0, x = 0

Therefore, both x and y intercept exist.

VII. Reciprocal

$y =\dfrac{1}x$

When $x = 0, y \rightarrow \infty$

Therefore, both x and y intercept do not exist.

VIII. Exponential

$y =b^x$

where b is any base:

When $x = 0, y =1$ therefore y intercept exists.

When we put y = 0, which is not possible

Therefore, both x and y intercept do not exist.

IX. Logarithmic

$y =logx$

When $x = 0, y \rightarrow$ not defined

Therefore, both x and y intercept do not exist.