Question

1. which graph fails the vertical line test?

a. a v - shaped graph ($y = |x|$)
b. a straight line
c. a parabola opening upwards
d. a circle

Explanation:

The vertical line test determines if a graph represents a function. A function has only one output (y - value) for each input (x - value). A circle's equation is \((x - h)^2+(y - k)^2 = r^2\), which can be solved for \(y\) as \(y=k\pm\sqrt{r^{2}-(x - h)^{2}}\). For a given \(x\) (within the domain of the circle), there are two possible \(y\) - values (one from the \(+\) and one from the \(-\) in the square root). The V - shaped graph (\(y = |x|\)), a non - vertical straight line (\(y=mx + b\), \(m
eq\infty\)), and a parabola opening upwards (\(y = ax^{2}+bx + c\), \(a>0\)) all pass the vertical line test because for each \(x\) there is only one \(y\).

Answer:

d. A circle