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45 votes
45 votes
Which equation is a function of x?

x = 5
x = y squared + 9
x squared = y
x squared = y squared + 16

User Evens
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1 Answer

22 votes
22 votes

Answer:

x squared = y

Explanation:

Functions

Things can get more complicated, but based on the examples given, for an equation to be a function of x, it must have a single y, where the y is not raised to a power.

Option 1: x=5

This equation doesn't have a y, so it isn't a function of x.

Option 2: x = y squared + 9

This equation has y raised to a power, so it isn't a function of x

Option 3: x squared = y

This equation has a y, and the y isn't raised to a power. This is a function of x.

Option 4: x squared = y squared + 16

This equation has y raised to a power, so it isn't a function of x

Determining functions graphically

If the equations are graphed, the graphs must pass a vertical line test (a vertical line drawn anywhere should not intersect the graph more than once).


Option 1: x=5

x=5 represents a vertical line, so it fails the vertical line test (the vertical line would overlap and intersect it infinitely many times).

Option 2: x = y squared + 9

x = y squared + 9 is a sideways parabola. A vertical line will cross it twice in several places

Option 3: x squared = y

x squared = y is a parabola that opens upward. It will pass the vertical line test

Option 4: x squared = y squared + 16

x squared = y squared + 16 is a hyperbola (fancy graph shape) that won't pass the vertical line test.

User Jeb
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