# ACT Math : How to find transformation for an analytic geometry equation

## Example Questions

### Example Question #2 : Transformation

If this is a sine graph, what is the phase displacement? 2π

4π

π

(1/2)π

0

0

Explanation:

The phase displacement is the shift from the center of the graph. Since this is a sine graph and the sin(0) = 0, this is in phase.

### Example Question #451 : Advanced Geometry

If this is a cosine graph, what is the phase displacement? 0

2π

4π

π

(1/2)π

π

Explanation:

The phase displacement is the shift of the graph. Since cos(0) = 1, the phase shift is π because the graph is at its high point then.

### Example Question #3 : Transformation

A regular pentagon is graphed in the standard (x,y) coordinate plane. Which of the following are the coordinates for the vertex P?       Explanation:

Regular pentagons have lines of symmetry through each vertex and the center of the opposite side, meaning the y-axis forms a line of symmetry in this instance. Therefore, point P is negative b units in the x-direction, and c units in the y-direction. It is a reflection of point (b,c) across the y-axis. ### Example Question #11 : Coordinate Geometry

If g(x) is a transformation of f(x) that moves the graph of f(x) four units up and three units left, what is g(x) in relation to f(x)?      Explanation:

To solve this question, you must have an understanding of standard transformations. To move a function along the x-axis in the positive direction, you must subtract the value from the operative x-value. For example, to move a function, f(x), five units to the left would be f(x+5).

To shift a function along the y-axis in the positive direction, you must add the value to the overall function. For example, to move a function, f(x), three units up would be f(x)+3.

The question asks us to move the function, f(x), left three units and up four units. f(x+3) will move the function three units to the left and f(x)+4 will move it four units up.

Together, this gives our final answer of f(x+3)+4.

### Example Question #21 : How To Find Transformation For An Analytic Geometry Equation

What is the period of the function? 2π

1

3π

π

4π

4π

Explanation:

The period is the time it takes for the graph to complete one cycle.

In this particular case we have a sine curve that starts at 0 and completes one cycle when it reaches .

Therefore, the period is ### All ACT Math Resources 