### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #1 : How To Find Transformation For An Analytic Geometry Equation

Give the equation graphed in the above figure.

**Possible Answers:**

**Correct answer:**

The graph below is the graph of the *absolute value function* , which pairs each -coordinate with its absolute value.

The given graph is the same as the above graph, except that each -coordinate is paired with the -coordinate three times that with which it is paired in the above graph. Therefore, the equation graphed is

or

### Example Question #2 : How To Find Transformation For An Analytic Geometry Equation

If the graph of the equation is shifted right three units on the coordinate plane, what will be the equation of the resulting graph?

**Possible Answers:**

**Correct answer:**

The graph of a function shifted right three units is the graph of . In this graph, , so the graph formed by the transformation is

The correct equation is .

### Example Question #3 : How To Find Transformation For An Analytic Geometry Equation

If the graph of the equation is reflected about the origin, what will the equation of the resulting graph be?

**Possible Answers:**

**Correct answer:**

The reflection of the graph of the equation about the origin is the graph of the equation , so replace with and with :

becomes

### Example Question #1 : How To Find Transformation For An Analytic Geometry Equation

If the graph of the equation is reflected about the -axis, what will the equation of the resulting graph be?

**Possible Answers:**

**Correct answer:**

The reflection of the graph of the equation about the -axis is the graph of the equation , so replace with :

becomes

### Example Question #5 : How To Find Transformation For An Analytic Geometry Equation

If the graph of the equation is reflected about the -axis, what will the equation of the resulting graph be?

**Possible Answers:**

**Correct answer:**

The reflection of the graph of the equation about the -axis is the graph of the equation , so replace with :

becomes

### Example Question #6 : How To Find Transformation For An Analytic Geometry Equation

If the graph of the equation is reflected about the origin, what will the equation of the resulting graph be?

**Possible Answers:**

None of the other responses gives a correct answer.

**Correct answer:**

The reflection of the graph of the equation about the origin is the graph of the equation , so replace with and with :

becomes

The absolute values of two expressions that are each other's opposites are equal, so is equivalent to . The expression can be rewritten as

.

### Example Question #1 : Transformation

Give the equation graphed in the above figure.

**Possible Answers:**

**Correct answer:**

The graph below is the graph of the *absolute value function* , which pairs each -coordinate with its absolute value.

The given graph is the above graph shifted right five units and upward three units. The graph of any function shifted right five units and upward three units is , so the correct response is .

### Example Question #8 : How To Find Transformation For An Analytic Geometry Equation

If the graph of the equation is shifted downward seven units on the coordinate plane, what will be the equation of the resulting graph?

**Possible Answers:**

**Correct answer:**

The graph of a function shifted downward seven units is the graph of . In this graph, , so the graph formed by the transformation is that of the equation

### Example Question #9 : How To Find Transformation For An Analytic Geometry Equation

Give the equation graphed in the above figure.

**Possible Answers:**

**Correct answer:**

The graph below is the graph of the absolute value function , which pairs each -coordinate with its absolute value.

The given graph is the above graph shifted right two units. The graph of shifted right two units is , so the correct response is .

### Example Question #10 : How To Find Transformation For An Analytic Geometry Equation

What equation is graphed in the above figure?

**Possible Answers:**

**Correct answer:**

The greatest integer function, or floor function, , pairs each value of with the greatest integer less than or equal to . Its graph is below.

The given graph is the above graph shifted downward four units. The graph of any function shifted downward four units is , so the given graph corresponds to equation .