Question

Identify which of the following equations represent functions. Select all that apply.

y = 4x + 13
x = 5
x2 + y2 = 16
y2 = One-thirdx - 6
y = 3x2 - x - 1

Answer 1

To determine which of the given equations represent functions, we need to check if each equation satisfies the definition of a function. A relation is a function if, for every input (usually x), there is exactly one output (usually y).

1. **y = 4x + 13**: This is a linear equation in slope-intercept form (y = mx + b). For every value of x, there is exactly one value of y. **This is a function.**

2. **x = 5**: This is a vertical line where x is always 5. For every y, x will always be 5. There are infinitely many y-values for a single x-value, which means this does not satisfy the function definition. **This is not a function.**

3. **x^2 + y^2 = 16**: This is the equation of a circle centered at the origin with a radius of 4. For most values of x (except at the extremes), there are two corresponding y-values for each x-value. Therefore, this does not represent a function. **This is not a function.**

4. **y^2 = (1/3)x - 6**: This represents a sideways parabola. For certain values of x, there could be two corresponding y-values (positive and negative roots). Thus, this does not meet the definition of a function. **This is not a function.**

5. **y = 3x^2 - x - 1**: This is a quadratic function. For every value of x, there is exactly one corresponding value of y. **This is a function.**

So, the equations that represent functions are:

- y = 4x + 13
- y = 3x^2 - x - 1