ACT Math : Algebra
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Example Questions
Example Question #74 : Graphing
Give the horizontal asymptote of the graph of the function
The graph has no horizontal asymptote.
We can rewrite this as follows:
This is a translation of the graph of 
Example Question #1 : How To Graph An Exponential Function
If the functions
were graphed on the same coordinate axes, what would be the 
Round to the nearest tenth, if applicable.
The graphs of 
We can rewrite the statements using 
To solve this, we can multiply the first equation by 
Example Question #2 : How To Graph An Exponential Function
If the functions
were graphed on the same coordinate axes, what would be the 
Round to the nearest tenth, if applicable.
The graphs of 
We can rewrite the statements using 
To solve this, we can set the expressions equal, as follows:
Example Question #451 : Advanced Geometry
If this is a sine graph, what is the phase displacement?
0
π
2π
4π
(1/2)π
0
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 #1 : How To Find Transformation For An Analytic Geometry Equation
If this is a cosine graph, what is the phase displacement?
2π
(1/2)π
π
0
4π
π
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 #1 : Transformation
A regular pentagon is graphed in the standard (x,y) coordinate plane. Which of the following are the coordinates for the vertex P?
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 #1 : Transformation
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)?
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 #2 : Transformation
What is the period of the function?
4π
2π
1
π
3π
4π
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
Example Question #1 : Linear / Rational / Variable Equations
n/17 = 54/9
What is the value of n?
None of the above.
85
93.5
54
102
102
Cross multiply: 9n = 54 * 17 → n = (54 * 17)/9 = 102.
This also can be solved by reducing the right hand side of the equation, so n/17 = 6.
Example Question #1 : Linear / Rational / Variable Equations
If 12x + 3 = 2(5x + 5) + 1, what is the value of x?
6
5
7
4
3
4
Starting with 12x + 3 = 2(5x + 5) + 1, we start by solving the parenthesis, giving us 12x + 3 = 10x + 11. We then subtract 10x from the right side and subtract three from the left, giving us 2x = 8; divide by 2 → x = 4.
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