# SAT Functions Review

# SAT Functions Review

In this blog, we’ll discuss common Functions. This is one of the topics on the SAT that tends to concern a lot of students. As we all know, a function relates an input value to an output value. It is usually denoted by the term f(x), or y. Of course, the letter denoting the function can be any letter at all: g(x), z(x), h(x), etc.

The most common functions are **y = x ^{2}, y = x^{3}, y = √x, y = x, y = |x|**

Let’s take a look at what these functions look like and how they are commonly manipulated:

**y = x**^{2}

^{2}

This is a classic function that is always tested. Know how to manipulate this function. Remember that the vertex is the lowest point and is at the axis of symmetry.

How do you flip the graph on the x-axis? You get the negative of the function!

**y = -x**^{2}

^{2}

How do you move the graph horizontally or vertically?

**——–** => **y = x**^{2 }+ 2

^{2 }+ 2

**——–** => **y = x**^{2 }– **2**

^{2 }–

# ——– => **y = (x – 2)**^{2 }

^{2 }

# ——– => **y = (x +2)**^{2}

^{2}

How do you stretch the graph or squeeze it?

**——–** => **y = x**^{2 }

^{2 }

**——–** => **y = 8x**^{2}

^{2}

# ——– => **y = 1/4(x)**^{2 }

^{2 }

# ——– => **y = 1/8(x)**^{2}

^{2}

**y = √x**

Yet another very common graph that’s seen on the SAT.

**——–** => **y = √x**

**——–** => **y = -√x**

Know how to flip it across the x-axis and the y-axis!

**——–** => **y = √x**

**——–** => **y = √-x**

# ——– => **y = -√x**

# ——– => **y = -√-x**

And of course, know how to move the graph along the x- and y -axes.

**——–** => **y = √(x – 2)**

**——–** => **y = √(x + 2)**

# ——– => **y = √x – 2**

# ——– => **y = √x + 2**

# y = x

This is also a very common function and necessary especially when you are doing equation of line questions. Know how to manipulate this function every way possible!

**——–** => **y = x**

**——–** => **y = -x**

# ——– => **y = x + 2**

# ——– => **y = x – 2**

**y = |x|**

This is the absolute value function.

**——–** => **y = ****|x|**

**——–** => **y = -|x|**

Again, know how to manipulate it on the horizontal and vertical axes.

# **——–** => **y = |x| (covered up by the yellow and blue)**

**——–** => **y = |x| – 2**

# ——– => **y = |x + 2|**

# ——– => **y = |x – 2|**

By now you should understand what you are expected to be able to do with the common functions. Try your skills with this function. What would you have to do to flip the equation on the x-axis? To move it to the right 2 spaces or left 2 spaces? To move it up 2 spaces, or down 2 spaces?

Functions can be tricky but with practice they become really easy. If you find that you’re having quite a bit of trouble understanding this topic as well as other topics in Algebra II – I highly recommend that you get **The New Math SAT Game Plan: The Strategic Way to Score Higher **by Philip Keller. This guy has won awards as a teacher and his book is one of the best for students who are having a hard time with basic SAT math. Remember, the best way to decrease your anxiety over math is to practice it so much that you become a pro at it. Next time, we’ll go over Number Properties – another very important aspect of the SAT.