Question

Which function matches g? Two hook shaped graphs, f and g, on a coordinate plane. The graph of f has three line segments: negative 2 comma 2 decreases to negative 1 comma negative 1 then horizontal to 1 comma 1, then increases to 2 comma zero. The graph of g has three longer line segments: negative 1 comma 4 decreases to zero comma negative 2, then horizontal to 2 comma negative 2, then increases to 3 comma zero. Group of answer choices g(x) = f(x – 2) g(x) = 2f(x – 1) g(x) = f(x – 1) g(x) = 2f(x – 2)

Answer 1

Answer:

Option (2).

Step-by-step explanation:

Coordinates of points A(-2, 2), B(-1, -1), C(-1, 4) and (0, -2)

By using formula to get the length of any segment having extreme ends at $(x_1,y_1)$ and $(x_2,y_2)$,

d = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Length of segment AB = $\sqrt{(-2+1)^2+(2+1)^2}$

                                      = $\sqrt{10}$ ≈ 3.16

Length of segment CD = $\sqrt{(0+1)^2+(-2-4)^2}$

                                      = $\sqrt{37}$ ≈ 6.08

Length of CD ≈ 2(length of AB)

But length of horizontal segments are equal.

Therefore, function 'f' is vertically stretched to form 'g'.

g(x) = 2f(x)

Now 'f' is translated by 1 unit right,

g(x) = 2f(x - 1)  

Option (2) will be the answer.