The intercepts are the points where the graph crosses the x or y-axis
- The x-intercepts changed from 0 to [tex]\±\sqrt 3[/tex].
- The y-intercepts changed from 0 to 3
The functions are given as:
[tex]f(x) = x^2[/tex]
[tex]g(x) = x^2 - 3[/tex]
Function f(x)
[tex]f(x) = x^2[/tex]
The x-intercept is calculated as follows:
Set f(x) to 0
[tex]x^2 = 0[/tex]
Solve for x
[tex]x = 0[/tex]
The y-intercept is calculated as follows:
Set x to 0
[tex]f(0) = 0^2[/tex]
[tex]f(0) = 0[/tex]
Hence, the intercepts are 0
Function g(x)
[tex]g(x) = x^2 - 3[/tex]
The x-intercept is calculated as follows:
Set g(x) to 0
[tex]x^2 - 3 = 0[/tex]
Solve for x
[tex]x^2 = 3[/tex]
[tex]x = \±\sqrt 3[/tex]
The y-intercept is calculated as follows:
Set x to 0
[tex]g(x) = x^2 - 3[/tex]
[tex]g(0) = 0^2 - 3[/tex]
[tex]g(0) = - 3[/tex]
The x-intercepts are [tex]\±\sqrt 3[/tex], while the y-intercept is -3
By comparing the intercepts of f(x) and g(x),
- The x-intercepts changed from 0 to [tex]\±\sqrt 3[/tex].
- The y-intercepts changed from 0 to 3
Read more about intercepts at:
https://brainly.com/question/3334417
