SAT Math Practice 1 - Shifting Functions
Original SAT Math problems are great to have. Students wanting to get into Dual Enrollment, like I did at Edison State College when I was in High School, have to take this and the ACT before they enroll in the college. Here is a short lesson and example on shifting functions.
Three of the Twelve Main Functions
These functions are called parent functions because we refer to them for any shifting graph problem. We need these to practice with, but the others all work the same and if you ever have trouble on these problems on the SAT, then just plug in three or four x-values and match the graphs manually.
The Squared Function
The Absolute Value Function
The Exponential Function
Short Lesson
The function we use to find shifts looks like this for each one:
- k is the letter that shifts x (left - and right +). We move our graph opposite the sign inside because in the equation it is negative. So if inside the parenthesis we have (x - 6) we would shift to the right 6.
- h is the letter that shifts y (up + and down -). We move our graph the same direction as the sign here. So, if we have our equation, say y = (x-6) + 1, we move the graph up 1.
- If there is a negative in front of the x, then flip the equation horizontally (reflect about y-axis)
- If there is a negative in front of the whole equation, then flip the equation vertically (reflect about x-axis)
Example 1 as a GIF
Graph the function 
Solution
Since there is a +3 with the x, then we shift left 3.
Since there is a -2 at the end, then we shift down 2.
Example 2
Graph the function 
Solution
There is no x-shift.
Since there is a -1 at the end of the equation, we shift up 1.
Since there is a - in front of the equation, we flip it over the y-axis.
SAT Math Problem (Solution Next Lesson)
I encourage you to try it, submit an answer and explanation in the comments for up-votes on your last few posts.
Graph the function 
