Question

Match each graph with its equation.
y = x^2
y= x^3
y = 1/ x^2
y = √x
y = x
y = ^3√x
y = 1 / x
y = |x|

Answer 1

To match each graph with its corresponding equation, consider how the characteristics of each function would translate graphically. Here's a brief description of each equation to help you match it to the right graph:

1. **y = x²**: This is a parabola that opens upwards. Its vertex is at (0,0) and it is symmetric about the y-axis.

2. **y = x³**: This cubic function has an S-shape curve that passes through the origin. It goes up to the right and down to the left, and is symmetric about the origin.

3. **y = 1/x²**: This function has two branches in the first and second quadrants, approaching the y-axis and x-axis asymptotically, but never touching them.

4. **y = √x**: This graph starts at the origin and curves upwards to the right. It is only defined for x ≥ 0, and is half of a sideways parabola.

5. **y = x**: A straight line with a slope of 1, passing through the origin. It bisects the first and third quadrants equally.

6. **y = ∛x (cube root of x)**: This function has a similar S-shape to y = x³, but it approaches the lines y = x and is defined for all x.

7. **y = 1/x**: This function has two branches, located in the first and third quadrants, and approaches both axes asymptotically.

8. **y = |x|**: This is a V-shaped graph centered at the origin, with straight lines extending in the first and second quadrants.

You can use these descriptions to match the graphs to the equations visually. Generally, you'd look for specific characteristics like the shape (linear, parabolic,) and the orientation (positive or negative slopes) to determine the correct match.