Question

13 multiple choice 1 point which of the following types of graphs represents a function? a circle a vertical line an oval a diagonal line increasing from left to right clear my selection

Explanation:

Step1: Recall the vertical line test

A graph represents a function if and only if every vertical line intersects the graph at most once.

Step2: Analyze each option

• Circle: A vertical line can intersect a circle at two points. For example, for the circle \(x^{2}+y^{2}=r^{2}\), the vertical line \(x = 0\) intersects the circle at \((0,r)\) and \((0, - r)\). So, a circle is not a function.
• Vertical line: A vertical line has the equation \(x = a\). For a vertical line, there are infinitely many \(y\) - values for a single \(x\) - value. By the definition of a function (a relation where each input \(x\) has exactly one output \(y\)), a vertical line is not a function.
• Oval: Similar to a circle, a vertical line can intersect an oval (ellipse) at two points. For the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} = 1\), the vertical line \(x=0\) intersects the ellipse at \((0,b)\) and \((0, - b)\). So, an oval is not a function.
• Diagonal line increasing from left to right: A diagonal line has an equation of the form \(y=mx + b\) where \(m

eq0\). For any vertical line \(x = k\), substituting \(x = k\) into \(y=mx + b\) gives \(y=mk + b\) (a single - valued output). Every vertical line will intersect the line \(y = mx + b\) at exactly one point.

Answer:

A diagonal line increasing from left to right.