Identify which of the following equations represent functions. Select all that apply. y=4x+13 x=5 x^2+y^2=16 y^2=(1)/(3)x-6 y=3x^2-x-1

To determine which of the given equations represent functions, we need to check if each equation defines a unique output (y-value) for every input (x-value). A relation is a function if, for every x-value in its domain, there is exactly one corresponding y-value.1. ** **: This is a linear equation in slope-intercept form , where m and b are constants. For every x-value, there is exactly one y-value. Therefore, this equation represents a function.2. ** **: This equation describes a vertical line, which means for the single x-value of 5, there can be multiple y-values. Thus, it does not pass the vertical line test and does not represent a function.3. ** **: This equation represents a circle with radius 4 centered at the origin. For some x-values, there are two corresponding y-values (one positive and one negative). Therefore, this equation does not represent a function.4. ** **: Solving for y gives . For some x-values, there are two possible y-values (positive and negative square roots). Hence, this equation does not represent a function.5. ** **: This is a quadratic equation in standard form . For every x-value, there is exactly one y-value. Therefore, this equation represents a function.In summary, the equations that represent functions are:- -