Question

HOW DO YOU SEE IT? Does the graph of $f$ represent inverse variation or direct variation?

A function labeled f is plotted on a coordinate plane. The x-axis is extended from negative 2 to 2, in increments of 2. The y-axis is extended from negative 4 to 4, in increments of 2. The function passes through points at ordered pair negative 1 comma negative 2 and ordered pair 2 comma 4.

Answer 1

the graph of f represents a direct variation

Explanation:

All direct variations are going to be linear functions, thus the graph of f represents a direct variation. However, I will give you a longer way to solve this problem, a more visual one, that will help understand this concept in an easier manner.

the basic formula for a direct variation is "y = k·x" and the basic formula for an inverse variation is "y =
`(k)/(x)`" (with k representing any costant)

we can solve this question by using the basic formulas to write inverse and direct variations, graph them, and see which one is the most similar to the one given in the question.

Since line f has a slope of 2, I decided to use 2 as the constant for both functions. Now we just substitute k for 2 in each function and graph it.

direct variation: y = 2x

inverse variation: y =
`(2)/(x)`

After re-writting the functions, I graphed them on desmos to see what they would look like. After comparing the original graph to the ones I created on Desmos, it can be seen that the red line graph (direct variation) is identical to the original one. Thus, the graph of f represents a direct variation.

p.s.: be familiar with teh formulas for direct and indirect variation, as they will be used a lot in the years to come (regaring math classes), even in AP Calculus

hope this helps! :)