All ACT Math Resources
Example Questions
Example Question #3 : How To Graph A Function
Which of the following graphs represents the y-intercept of this function?
Graphically, the y-intercept is the point at which the graph touches the y-axis. Algebraically, it is the value of when .
Here, we are given the function . In order to calculate the y-intercept, set equal to zero and solve for .
So the y-intercept is at .
Example Question #15 : How To Graph A Function
Which of the following graphs represents the x-intercept of this function?
Graphically, the x-intercept is the point at which the graph touches the x-axis. Algebraically, it is the value of for which .
Here, we are given the function . In order to calculate the x-intercept, set equal to zero and solve for .
So the x-intercept is at .
Example Question #4 : How To Graph A Function
Which of the following represents ?
A line is defined by any two points on the line. It is frequently simplest to calculate two points by substituting zero for x and solving for y, and by substituting zero for y and solving for x.
Let . Then
So our first set of points (which is also the y-intercept) is
Let . Then
So our second set of points (which is also the x-intercept) is .
Example Question #1 : How To Graph A Function
Suppose .
To obtain the graph of , shift the graph a distance of units .
Up and right
To the left
To the right
Upwards
Downwards
Upwards
There are four shifts of the graph y = f(x):
y = f(x) + c shifts the graph c units upwards.
y = f(x) – c shifts the graph c units downwards.
y = f(x + c) shifts the graph c units to the left.
y = f(x – c) shifts the graph c units to the right.
Example Question #171 : Graphing
Which of the following graphs does NOT represent a function?
All of the graphs are functions.
This question relies on both the vertical-line test and the definition of a function. We need to use the vertical-line test to determine which of the graphs is not a function (i.e. the graph that has more than one output for a given input). The vertical-line test states that a graph represents a function when a vertical line can be drawn at every point in the graph and only intersect it at one point; thus, if a vertical line is drawn in a graph and it intersects that graph at more than one point, then the graph is not a function. The circle is the only answer choice that fails the vertical-line test, and so it is not a function.
Example Question #1 : How To Graph A Point
How would you plot the point ?
From the origin, go right units, and up units
From the origin, go up units, and right units
From the origin, go left units, and up units
From the origin, go right units, and down units
From the origin, go right units, and up units
For the ordered pair
The first number is for the x-axis, so because it is positive you go right .
The second number is for the y-axis, so because it is positive you go up .
Example Question #2 : How To Graph A Point
How would you plot the point ?
From the origin, go left units, and up units
From the origin, go right units, and up units
From the origin, go left units, and down units
From the origin, go right units, and down units
From the origin, go left units, and up units
For the ordered pair we would do the following.
The first number is for the x-axis, so because it is negative you go left units.
The second number is for the y-axis, so because it is positive you go up units.
Example Question #3 : How To Graph A Point
In which Quadrant is the point located?
Quadrant I
Quadrant III
Quadrant II
Quadrant IV
Quadrant III
To find out which quadrant a point lives in, we need to remember the qualities of each quadrant. By qualities, I mean the signs associated with the x and y values which are dependent on the quadrant the point resides in.
All coordinate pairs that are in Quadrant I will have a positive x value and a positive y value.
All coordinate pairs that are in Quadrant II will have a negative x value and a positive y value.
All coordinate pairs that are in Quadrant III will have a negative x value and a negative y value.
All coordinate pairs that are in Quadrant IV will have a positive x value and a negative y value.
For the point we see that both the x and y values are negative therefore, the point lies in the third quadrant. We can also check this by starting from the origin and going left 3 units and down 3 units. This will end up in the lower-left section of the coordinate-plane, which is Quadrant III.
Example Question #1 : How To Graph A Point
What are the coordinates of point B?
Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is .
Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is .
is then the coordinate of the point.
Example Question #2 : How To Graph A Point
What are the coordinates for point A?
Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is .
Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is .
are the coordinates for point A.