Question 146·Medium·Nonlinear Functions
The graph of is shown in the coordinate plane. A point is labeled on the graph.
Which choice gives the coordinates of the point on the graph of that corresponds to point ?
For transformation-of-graph questions, treat a labeled point on as your anchor. Then apply each part of the new function in order: inside changes affect (for , move right by ), and outside changes affect (a leading minus reflects across the -axis; adding a constant shifts up or down).
Hints
Find the coordinates of
Use the grid to read the - and -coordinates of the labeled point .
Handle the horizontal shift
In , subtracting 3 inside the function moves points to the right. Think about what happens to the -coordinate.
Handle the changes to
The minus sign in front changes the sign of every -value, and then the adjusts it again. Apply both changes to the -coordinate of .
Desmos Guide
Enter the coordinates of point
From the graph, create a point by typing A=(x_A,y_A) and set and to match the labeled point.
Compute the transformed coordinates
In Desmos, define
x2 = x_A + 3y2 = -y_A + 1
Plot the transformed point and match a choice
Plot B=(x2,y2). Compare point 's coordinates to the four answer choices and select the one that matches.
Step-by-step Explanation
Read point from the graph
From the labeled point on the graph, .
Interpret the transformation
For :
- shifts the graph of right 3 units, so increases by 3.
- The negative sign reflects outputs across the -axis, so becomes .
- The shifts outputs up 1 unit, so becomes .
Transform the point
Starting from :
- New :
- New :
So the corresponding point is .