Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x) + 20?
The graph of y = f(x) will shift left 20 units.
The graph of y = f(x) will shift down 20 units.
The graph of y = f(x) will shift up 20 units.
The graph of y = f(x) will shift right 20 units.
Choose the equation below that represents the line that passes through the point (−2, −1) and has a slope of 5.
y − 1 = 5(x − 2)
y + 1 = 5(x + 2)
y + 2 = 5(x + 1)
y − 2 = 5(x − 1)
and this one
On the first one, all you are doing is adding 20 to f(x), which just adds 20 to y. So, the graph shifts up 20.
Use the point-slope form of the line:
y - (-1) = 5(x - (-2))
or
y + 1 = 5(x+2)
The correct statement is:
The graph of y = f(x) will shift up 20 units.
To determine the effect of replacing the graph of y = f(x) with the graph of y = f(x) + 20, we need to understand how changing the equation affects the position of the graph.
The equation y = f(x) represents the graph of the function f(x). The addition of 20 to f(x) as y = f(x) + 20 means that every y-coordinate on the graph will be increased by 20 units.
Therefore, the correct statement is: The graph of y = f(x) will shift up 20 units.
To understand this visually, imagine a point on the original graph at (x, y). After adding 20 to y, the new y-coordinate will be y + 20. Consequently, the entire graph will be shifted upward by 20 units.