Evaluate the expression below for x = 4 6 (x +7)
1 answer:
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Option d: reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up.
Step-by-step explanation:
The parent function is
The transformation function is
In the transformed function, the function is added +2, which shifts the graph by 2 units up.
Also, the function is multiplied by 3, which stretches the function vertically by a factor of 3 units.
The variable x is multiplied by -1, such that the function reflects across y-axis.
Thus, the correct answer is option d.
The graph is attached below which shows the parent function and the transformed function.
The transformation function is reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up.
I'm thinking this is what the problem looks like: 
. The first thing to do is to move the 
over to the other side because it has a common denominator with the other side. Doing that and at the same time combining them over their common denominator looks like this: 
. The best way to solve for x now is to cross-multiply to get 3(4-x)=-4(x-4). Distributing through the parenthesis is 12 - 3x = -4x + 16. Solving for x gives us x = 4. Of course when we sub a 4 back in for x we get real problems, don't we? Dividing by zero breaks every rule in math that there ever was! So, yes, the solution is extraneous.