Question

Given each of the following parent functions below:

1. f(x) = 23
II. f (x) = |ac
III. f (x) = 2
IV. f (x) = 22
V. f (x) = 1
Which of the above parent functions have the x-intercept and y-intercept at the origin?
OF. I, II, and III
O G. I, II, and V
H. All of them
J. I and II only

Answer 1

The parent functions that have the x-intercept and y-intercept at the origin are II. f(x) = |x| and III. f(x) = 2.

Step-by-step explanation:

To determine which of the given parent functions have the x-intercept and y-intercept at the origin, we need to look at the equations and see if they satisfy the conditions. The x-intercept occurs when the value of y is 0, and the y-intercept occurs when the value of x is 0.

Let's analyze each parent function:

1. f(x) = 2
2. 
   
3. 
   
4. This function is a horizontal line passing through the point (0, 2). It does not have its x-intercept or y-intercept at the origin.
5. 
   
6. 
   
7. f(x) = |x|
8. 
   
9. 
   
10. This function is a V-shaped graph that passes through the origin. It has both the x-intercept and y-intercept at the origin.
11. 
    
12. 
    
13. f(x) = 22
14. 
    
15. 
    
16. This function is a horizontal line passing through the point (0, 22). It does not have its x-intercept or y-intercept at the origin.
17. 
    
18. 
    

Based on the analysis, the parent functions that have the x-intercept and y-intercept at the origin are II. f(x) = |x| and III. f(x) = 2.