Answer:
D. f(-1/2x)
Step-by-step explanation:
We can answer this by a process of elimination or POE
Given a graph f we are asked to find a transformation g in terms of f
1. The graph f is that of a downward facing parabola which represents a quadratic equation. We can see the vertex is at (2, -1)
2. g is also a downward facing parabola We see the vertex is at (-4, -1)
Also note that the y-intercepts of both graphs is at y = -2. The y-intercept is the value of y where the graph cuts the y-axis. In other words, it is the value of y when x = 0.
Therefore both graphs have y-intercepts at (0, -2)
Neither of the above two statements 1 and 2 is really needed to answer this question - I just put it out there for your understanding
First, we can eliminate choices A and C directly. Putting a negative sign in front of a function will change the function graph from a downward parabola to an upward parabola. Since both f and g are downward parabolas, they both have the same sign
That leaves us with choices B and D
We see that for the same values of y, the x values are doubled with a negative sign added
This means that that the coefficient of x must be negative less than 1
Hence D is the correct answer
