Question
Which graph represents y as a function of x?
a.The graph shows a straight line passing through the origin (0,0) with a positive slope (this is the shape ' / ' )
b. this graph shows a |
c. The graph shows a triangle plotted on the coordinate plane.
d. The graph shows a semicircle centered at the origin (0,0) with a radius of 3. (its like a kodak seed from legends of zelda shape or a odd tear drop shape.)
a.The graph shows a straight line passing through the origin (0,0) with a positive slope (this is the shape ' / ' )
b. this graph shows a |
c. The graph shows a triangle plotted on the coordinate plane.
d. The graph shows a semicircle centered at the origin (0,0) with a radius of 3. (its like a kodak seed from legends of zelda shape or a odd tear drop shape.)
Answers
GPT-4o mini
To determine which graph represents \( y \) as a function of \( x \), we can use the vertical line test. A vertical line will intersect a graph at most once if the graph represents \( y \) as a function of \( x \).
Let's analyze each option:
a. **A straight line passing through the origin (0,0) with a positive slope (this is the shape ' / ')**
- This is a linear function, and for any value of \( x \), there is exactly one corresponding value of \( y \). **This represents \( y \) as a function of \( x \).**
b. **The graph shows a vertical line ( | )**
- A vertical line fails the vertical line test because it intersects the line at infinitely many points for the same \( x \) value. **This does not represent \( y \) as a function of \( x \).**
c. **The graph shows a triangle plotted on the coordinate plane.**
- Depending on the specific configuration of the triangle, it may intersect some vertical lines in more than one point, meaning some values of \( x \) could correspond to multiple values of \( y \). Therefore, **it may not represent \( y \) as a function of \( x \).**
d. **The graph shows a semicircle centered at the origin (0,0) with a radius of 3.**
- A semicircle will also fail the vertical line test, as a vertical line can intersect the semicircle at two points for certain values of \( x \) within the range of the semicircle. **This does not represent \( y \) as a function of \( x \).**
Based on the analysis, the graph that represents \( y \) as a function of \( x \) is:
**a. The graph shows a straight line passing through the origin (0,0) with a positive slope.**
Let's analyze each option:
a. **A straight line passing through the origin (0,0) with a positive slope (this is the shape ' / ')**
- This is a linear function, and for any value of \( x \), there is exactly one corresponding value of \( y \). **This represents \( y \) as a function of \( x \).**
b. **The graph shows a vertical line ( | )**
- A vertical line fails the vertical line test because it intersects the line at infinitely many points for the same \( x \) value. **This does not represent \( y \) as a function of \( x \).**
c. **The graph shows a triangle plotted on the coordinate plane.**
- Depending on the specific configuration of the triangle, it may intersect some vertical lines in more than one point, meaning some values of \( x \) could correspond to multiple values of \( y \). Therefore, **it may not represent \( y \) as a function of \( x \).**
d. **The graph shows a semicircle centered at the origin (0,0) with a radius of 3.**
- A semicircle will also fail the vertical line test, as a vertical line can intersect the semicircle at two points for certain values of \( x \) within the range of the semicircle. **This does not represent \( y \) as a function of \( x \).**
Based on the analysis, the graph that represents \( y \) as a function of \( x \) is:
**a. The graph shows a straight line passing through the origin (0,0) with a positive slope.**
correct!