Question

Determine which of the following statements are true for the given parent function.
-4
-2
2
4
-4
-2
2
4
x
y



x y graph
Question content area bottom
Part 1
Select all that apply.
A.
Approaches infinity as x increases
B.
Is defined for all real numbers
C.
Has no curvature
D.
Has no​ x-intercept

Answer 1

I can’t tell which parent function you mean from the text/diagram you posted. Could you either

- paste the equation (for example y = x, y = x^2, y = 1/x, y = |x|, y = e^x, etc.), or
- attach or describe the graph more fully (shape, intercepts, asymptotes)?

Meanwhile, here are quick rules you can use to check each statement for a given parent function:

- A (Approaches infinity as x increases): true if f(x) → +∞ as x → +∞ (e.g. y = x, x^2, x^3, e^x). False for functions that approach a finite limit or 0 (e.g. 1/x → 0).
- B (Is defined for all real numbers): true for polynomials, y = x, x^2, x^3, e^x, |x|. False for y = 1/x (undefined at 0) or y = √x (undefined for x < 0).
- C (Has no curvature): true only for straight lines (e.g. y = x or y = mx + b). False for polynomials of degree ≥ 2, reciprocals, exponentials, absolute value at the cusp, etc.
- D (Has no x-intercept): true if the function never equals 0 (e.g. y = e^x, y = 1/x). False if it crosses/touches the x-axis (e.g. y = x has intercept at 0).

If you tell me which parent function (or upload the graph), I’ll mark which options are correct.