The graph of a function f(x) is moved to obtain the function g(x)
. Which of the following functions represent g(x)
? Select the two correct answers.
Two lines are graphed on a four quadrant coordinate plane. The horizontal x-axis and the vertical y-axis go from negative 5.5 to 5.5 in increments of 1. The first line labeled g left parenthesis x right parenthesis passes through left parenthesis negative 2 comma 0 right parenthesis and left parenthesis 0 comma negative 1 right parenthesis. The second line labeled f left parenthesis x right parenthesis passes through left parenthesis 0 comma 1 right parenthesis and left parenthesis 2 comma 0 right parenthesis.
(1 point)
Responses
f(x)+2
f left parenthesis x right parenthesis plus 2
f(x+4)
f left parenthesis x plus 4 right parenthesis
f(x+2)
f left parenthesis x plus 2 right parenthesis
f(x)−2
f left parenthesis x right parenthesis minus 2
f(x−4)
The correct answers are:
1) f(x) + 2 or f(x) plus 2
2) f(x-4)
To find the function g(x), we need to analyze how the original function f(x) has been moved.
From the information given, we can see that the original function f(x) passes through the points (-2, 0) and (0, -1), while the new function g(x) passes through the points (0, 1) and (2, 0).
In order to move the graph from f(x) to g(x), we can observe that the graph has been shifted horizontally by 2 units to the right and vertically by 1 unit up.
Therefore, the correct functions that represent g(x) are:
1. f(x+2) - This represents a horizontal shift of 2 units to the right.
2. f(x) + 2 - This represents a vertical shift of 2 units up.
So the correct answers are:
- f(x+2)
- f(x) + 2
To determine the function g(x), we need to understand how the graph of f(x) is moved.
Looking at the information provided, we see that the graph of the first line, g(x), passes through (-2, 0) and (0, -1), while the graph of the second line, f(x), passes through (0, 1) and (2, 0).
To move the graph of f(x), we need to make corresponding adjustments to the x and y-values of the points on the graph.
Option 1: f(x) + 2
This would shift the graph of f(x) vertically upward by 2 units compared to g(x). However, this does not match the given information about the points (-2, 0) and (0, -1) on g(x). Thus, this option is incorrect.
Option 2: f(x+4)
This would shift the graph of f(x) horizontally to the left by 4 units compared to g(x). However, this does not match the given information about the points (-2, 0) and (0, -1) on g(x). Thus, this option is incorrect.
Option 3: f(x+2)
This would shift the graph of f(x) horizontally to the left by 2 units compared to g(x). This matches the given information about the points (-2, 0) and (0, -1) on g(x). Thus, this option is correct.
Option 4: f(x) - 2
This would shift the graph of f(x) vertically downward by 2 units compared to g(x). However, this does not match the given information about the points (-2, 0) and (0, -1) on g(x). Thus, this option is incorrect.
Option 5: f(x-4)
This would shift the graph of f(x) horizontally to the right by 4 units compared to g(x). However, this does not match the given information about the points (-2, 0) and (0, -1) on g(x). Thus, this option is incorrect.
Therefore, the two correct answers are:
- f(x+2)
- f(x)−2