Does the graph represent a function? Khan Academy

Mathematics

2 answers:

Ierofanga [76]2 years ago

7 0

Answer:

yes

Step-by-step explanation:

try using a vertical line, if you move the vertical line across the graph and the line touches the graph only at one point, than it means it is a function

serg [7]2 years ago

6 0

Answer:

This graph represents a function

Step-by-step explanation:

By its definition, a function is a relation or a correlation between two sets (groups) of values where every input corresponds to only one output. What this means is that every input in a function can only have one output. This characteristic results in a unique property in the graph of a function, that is, the verticle line test. The verticle line test states that when one draws a line through the graph of a function, the line can only intersect the graph in exactly one place in the function. If the line intersects the graph in more than one place, then the graph does not represent a function. In the given situation, any verticle line drawn on the graph only intersects the graph in one place, thus the graph represents a function.

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Please show me how you got the answer thanks.

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kirza4 [7]

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Dafna11 [192]

Keeping in mind that x = rcos(θ) and y = rsin(θ).

we know the magnitude "r" of U and V, as well as their angle θ, so let's get them in standard position form.

$\bf u=
\begin{cases}
x=7cos(330^o)\\
\qquad 7\cdot \frac{\sqrt{3}}{2}\\
\qquad \frac{7\sqrt{3}}{2}\\
y=7sin(330^o)\\
\qquad 7\cdot -\frac{1}{2}\\
\qquad -\frac{7}{2}
\end{cases}\qquad \qquad v=
\begin{cases}
x=8cos(30^o)\\
\qquad 8\cdot \frac{\sqrt{3}}{2}\\
\qquad \frac{8\sqrt{3}}{2}\\
y=8sin(30^o)\\
\qquad 8\cdot \frac{1}{2}\\
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\end{cases}$

$\bf u+v\implies \left( \frac{7\sqrt{3}}{2},-\frac{7}{2} \right)+\left( \frac{8\sqrt{3}}{2},4 \right)\implies \left( \frac{7\sqrt{3}}{2}+\frac{8\sqrt{3}}{2}~~,~~ -\frac{7}{2}+4\right)
\\\\\\
\left(\stackrel{a}{\frac{15\sqrt{3}}{2}}~~,~~ \stackrel{b}{\frac{1}{2}}\right)\\\\
-------------------------------$

$\bf tan(\theta )=\cfrac{b}{a}\implies tan(\theta )=\cfrac{\frac{1}{2}}{\frac{15\sqrt{3}}{2}}\implies tan(\theta )=\cfrac{1}{15\sqrt{3}}
\\\\\\
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Does the graph represent a function? Khan Academy​

Does the graph represent a function? Khan Academy