Question

match each table with its equation
y=x^2
y=x^3
y=x
y=|x|
y=√x
y=1/x
a. input -2 -1 0 1 2 3
output -2 -1 0 1 2 3
B. input -2 -1 0 1 2 3
output -0.5 1 _ 1 0.5 0.33
c. input -2 -1 0 1 2 3
output -8 -1 0 1 8 27
d. input -2 -1 0 1 2 3
output 4 1 0 1 4 9
e. input -2 -1 0 1 4 9
output _ _ 0 1 2 3
f input -2 -1 0 1 2 3
output 2 1 0 1 2 3

Answer 1

Let's match each table with its corresponding equation.

1. **y = x**: This is a linear function where the output is the same as the input.
- **Match: a.**
- Input: -2 -1 0 1 2 3
- Output: -2 -1 0 1 2 3

2. **y = x^2**: This is a quadratic function where the output is the square of the input.
- **Match: d.**
- Input: -2 -1 0 1 2 3
- Output: 4 1 0 1 4 9

3. **y = x^3**: This is a cubic function where the output is the cube of the input.
- **Match: c.**
- Input: -2 -1 0 1 2 3
- Output: -8 -1 0 1 8 27

4. **y = |x|**: This is an absolute value function where the output is the non-negative value of the input.
- **Match: e.**
- Input: -2 -1 0 1 4 9
- Output: _ _ 0 1 2 3 (corrected variable values: 2 1 0 1 2 3)

5. **y = √x**: This is the square root function; values are defined for x ≥ 0.
- **Match: f.**
- Input: -2 -1 0 1 2 3
- Output: 2 1 0 1 2 3

6. **y = 1/x**: This is a hyperbolic function. Values tend to infinity as x approaches 0, and we generally do not include zero as input.
- **Match: b.**
- Input: -2 -1 0 1 2 3
- Output: -0.5 1 _ 1 0.5 0.33

So the matches are:

- a → y = x
- b → y = 1/x
- c → y = x^3
- d → y = x^2
- e → y = |x|
- f → y = √x

Note: Ensure to confirm or adjust the outputs to match the functions accurately!