Transform the parent function y=sin x until it maps onto the given graph.
B
b
Transform the parent function y=cos x until it maps onto the given graph.
C
c
Transform the parent function y=cos x until it maps onto the given graph.
D
d
Transform the parent function y=sin x until it maps onto the given graph.
A
a
y=sin(x-π/4)+2
B
b
y=3/2cos x+0.5
C
c
y=cos(x+π/3)+2
D
d
y=-3sin(x+π/3)-1
Practice makes perfect
a
To find an equation for the given graph, we have to transform one of the parent functions y=cos x or y=sin x until it maps onto the given graph. The graph resembles the sine function the most. Therefore, we will use this as our parent function.
The first thing we notice is that the given graph is above the parent function. This means we have to translate y=sin x upwards. To determine by how much, we should add the midline to both graphs.
As we can see, the midline of the given graph is at y=2 while it's y=0 for the parent function. Therefore, to give them the same vertical position, we have to add 2 to y=sin x.
Comparing the translated parent graph and the given graph, we notice that the given graph is π4 units to the right of y=sin x+2. Therefore, we need to subtract π4 from x to make them map onto each other.
b
Like in Part A, we have to pick one of the parent functions, y=cos x or y=sin x, and transform it until it maps onto the function. Examining the given graph, we notice that it resembles y=cos x the most.
The graphs have different vertical positions. This means we have to translate y=cos x upwards. To determine by how much, we should add the graph's respective midlines.
The midline of the given graph is y=0.5 and it is y=0 for the parent function. To give them the same vertical position, we have to add 0.5 to y=cos x.
To complete the transformation, we also have to give them the same amplitude. The translated parent function has an amplitude of 1, while it is 1.5 for the given graph. Therefore, to complete the transformation we have to multiply cos x by 32.
c
Similar to Part B, we think it resembles the parent function y=cos x the most. Therefore, this is the parent function we will transform.
The first thing we notice is that the graphs have different vertical positions. This means we have to translate y=cos x upwards. To determine by how much, we should draw the graph's respective midlines.
The midline of the given graph is at y=2, while it is y=0 for the parent function. To give them the same vertical position, we have to add 2 to y=cos x.
Comparing the translated parent graph and the given graph, we see that the given graph is π3 units to the left of y=cos x+2. Therefore, we have to add π3 to x to make them map onto each other.
d
The graph resembles an inverted sine function. Therefore, we will use y=sin x as our parent function.
Like in previous parts, we should first find the midlines of the respective graphs.
The midline of the given graph is at y=- 1, while it is y=0 for the parent function. To give them the same vertical position, we have to subtract 1 from y=sin x.
The translated parent function has an amplitude of 1, while it is 3 for the desired function. As already mentioned, the given graph resembles an inverted sine function. To make sure that we invert the parent function, we have to multiply sin x by - 3.
Comparing the transformed parent graph and the given graph, we notice that the given graph is π3 units to the left of y=- 3sin x-1. Therefore, we need to add π3 to x to make them map onto each other.
