Can somebody help me with this one. It says use the vertical line test to determine which graph represents a function

Only option C shows a function

Step-by-step explanation:

The vertical line test is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y, for each unique input, x. This means that a vertical line made in the domain of the function can crosses the curve of the function only once. If it crosses the curve of the function more than once, then the curve is not a function.

In option A, a vertical line would cross two values, so it is not a function.

The curve of option B is a vertical line itself, so a vertical line would intersect an infinite amount of points; then it is not a function.

Option C is a function because a vertical line would only intersect the function's curve (which is a line) once.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.