How is g(x) =1/2x-4
from the parent graph ƒ(x) =1/x
A) Vertically stretched by a factor of 2 and shifted right 2 units.
B) Horizontally stretched by a factor of 2 and shifted right 4 units.
C) Vertically compressed by a factor of 1/2
and shifted left 2 units.
D) Vertically compressed by a factor of 1/2
and shifted right 2 units. <my answer
To determine how the function g(x) is derived from the parent graph ƒ(x) = 1/x, we can analyze the equation g(x) = 1/2x - 4.
First, let's compare the structure of the two equations. In the parent graph ƒ(x) = 1/x, the variable x is in the denominator, implying that the graph is a reciprocal function.
Now, let's consider the equation g(x) = 1/2x - 4. The equation includes a constant factor of 1/2 multiplied by x, which shows that the graph of g(x) has been horizontally stretched by a factor of 2. This means that the function g(x) is wider than ƒ(x) but retains the same shape.
Next, we observe that the equation subtracts 4 from the function 1/2x. Therefore, the entire graph of g(x) is shifted downwards by 4 units. The shift downward implies that the y-values of g(x) are smaller than the corresponding y-values of ƒ(x).
Considering the analysis above, we can conclude that the function g(x) = 1/2x - 4 is horizontally stretched by a factor of 2 and shifted downward by 4 units from the parent graph ƒ(x) = 1/x.
While your option D suggests a vertical compression, the actual transformation is a horizontal stretch. So, the correct answer is B) Horizontally stretched by a factor of 2 and shifted right 4 units.
take a look at the graphs, and it should be clear. Or, study your text and apply the rules.
http://www.wolframalpha.com/input/?i=plot+y%3D1%2Fx,+y%3D1%2F(2x-4)