Asked by Andrea Noriega on May 19, 2024
Verified
Sketch a graph of the equation −6x+7y=42- 6 x + 7 y = 42−6x+7y=42 . Use the Vertical Line Test to determine whether y is a function of x .
A) y is a function of x . 
B) y is not a function of x . 
C) y is a function of x . 
D) y is not a function of x . 
E) y is a function of x . 
Vertical Line Test
A method to determine if a graph represents a function by checking if any vertical line intersects the graph at more than one point.
Function
In mathematics, a relation between sets that associates every element of a first set to exactly one element of the second set.
- Comprehend and utilize the vertical line test on graphs to ascertain whether a relation qualifies as a function.
- Carry out modifications on fundamental functions such as linear, quadratic, and absolute value functions.
Verified Answer
0:
0000001596 : Ahmad Abdulla Yousuf Albudoor AlfalasiMay 25, 2024
Final Answer :
C
Explanation :
To graph the equation, we can begin by finding the x and y-intercepts:
-When x equals 0, 7y = 42, so y = 6. When y equals 0, -6x = 42, so x = -7.
-We can plot these points and connect them with a straight line.
-Then, we can use the Vertical Line Test to determine whether y is a function of x. If every vertical line intersects the graph at most once, then the graph represents a function. Looking at the graph of the equation, we can see that every vertical line intersects the graph at most once, so y is a function of x.
-When x equals 0, 7y = 42, so y = 6. When y equals 0, -6x = 42, so x = -7.
-We can plot these points and connect them with a straight line.
-Then, we can use the Vertical Line Test to determine whether y is a function of x. If every vertical line intersects the graph at most once, then the graph represents a function. Looking at the graph of the equation, we can see that every vertical line intersects the graph at most once, so y is a function of x.
Learning Objectives
- Comprehend and utilize the vertical line test on graphs to ascertain whether a relation qualifies as a function.
- Carry out modifications on fundamental functions such as linear, quadratic, and absolute value functions.