Question

question 2 (1 point) saved

the base function \\(y = x\\) is translated 2 units to the left and 2 units up. if the graphs of the original function and base function were placed on the same grid,

a) the transformed function would be to the right of the base function

b) the transformed function would be to the left of the base function

c) the two functions would overlap

d) the transformed function would be below the base function

Explanation:

Determine the equation of the transformed function

Using the Function Transformations knowledge point

$$
LATEXBLOCK0
$$

Compare the positions of the two functions

To find the relative horizontal position, we compare the \(x\)-intercepts of both lines:

• For the base function \(y = x\), the \(x\)-intercept is at \((0, 0)\).
• For the transformed function \(y = x + 4\), setting \(y = 0\) gives \(x = -4\), so the \(x\)-intercept is at \((-4, 0)\).

Since \(-4 < 0\), the graph of the transformed function lies to the left of the base function.

Match with the given options

Comparing the relative positions of the graphs:

• Option A states the transformed function is to the right, which is incorrect.
• Option B states the transformed function is to the left, which is correct.
• Option C states they overlap, which is incorrect.
• Option D states the transformed function is below, which is incorrect (it is 4 units above).

Answer:

• A) the transformed function would be to the right of the base function
• B) the transformed function would be to the left of the base function (Correct answer)
• C) the two functions would overlap
• D) the transformed function would be below the base function