Explain how the following graphs are obtained from the graph of y=f(x). (Select all that apply.)
(a) y=7f(x)
shifts 7 units upward
shifts 7 units downward
shifts 7 units to the right
shifts 7 units to the left
stretch the graph vertically by a factor of 7
shrink the graph vertically by a factor of 7
stretch the graph horizontally by a factor of 7
shrink the graph horizontally by a factor of 7
reflect about the x-axis
reflect about the origin
(b) y= f(x-4)
shift 4 units upward
shift 4 units downward
shift 4 units to the right
shift 4 units to the left
stretch the graph vertically by a factor of 4
shrink the graph vertically by a factor of 4
stretch the graph horizontally by a factor of 4
shrink the graph horizontally by a factor of 4
reflect about the x-axis
reflect about the origin
(c) y= -f(x)
shift 1 unit upward
shift 1 unit downward
shift 1 unit to the right
shift 1 unit to the left
stretch the graph vertically by a factor of 1
shrink the graph vertically by a factor of 1
stretch the graph horizontally by a factor of 1
shrink the graph horizontally by a factor of 1
reflect about the x-axis
reflect about the origin
(a) stretch the graph vertically by a factor of 7
(b) shift 4 units to the right
(c) reflect about the x-axis
You offered no ideas here or on your next post. If you truly are lost, you will do well to review your text, and google examples and explanations.
(a) The graph of y=7f(x) stretches the graph vertically by a factor of 7.
(b) The graph of y=f(x-4) shifts the graph 4 units to the right.
(c) The graph of y=-f(x) reflects the graph about the x-axis.
(a) To obtain the graph of y = 7f(x) from the graph of y = f(x):
- Stretch the graph vertically by a factor of 7.
(b) To obtain the graph of y = f(x-4) from the graph of y = f(x):
- Shift the graph 4 units to the right.
(c) To obtain the graph of y = -f(x) from the graph of y = f(x):
- Reflect the graph about the x-axis.
(a) y=7f(x):
- To obtain this graph, you would stretch the graph vertically by a factor of 7. This means that each point on the original graph is multiplied by 7 in the y-direction.
- None of the other options apply to this case.
(b) y=f(x-4):
- To obtain this graph, you would shift the graph 4 units to the right. This means that each point on the original graph is moved horizontally 4 units to the right.
- None of the other options apply to this case.
(c) y=-f(x):
- To obtain this graph, you would reflect the graph about the x-axis. This means that each point on the original graph is replaced by its reflection across the x-axis.
- None of the other options apply to this case.