Vertical line test states that a vertical line needs to cuts the graph of a function(equation) at only one point, for it to represent a function.
If the graph of the equation represented in the coordinate axis, is cut by the vertical line at more than one point, then the graph is not a function.
State the domain and range for each graph and then tell if the graph is a function.
Problem 1 :
Solution :
Writing the points marked above, we get
(-3, -4) (-2, 5) (1, 3) (1, -2) (4, 0)
Domain = {-3, -2, 1, 4}
Range = {-4, -2, 0, 3, 5}
Here 1 is having more than one output, it is not a function.
Problem 2 :
Solution :
Between -3 to 3, the graph is spreading over the x-axis.
Domain = -3 ≤ x ≤ 3
Between -4 to 3, the graph is spreading over the y-axis.
Range = -4 ≤ y ≤ 3
By drawing the vertical line, that will intersect the curve at more than one point. So, it is not a function.
Problem 3 :
Solution :
Between -4 to ∞, the graph is spreading over the x-axis. Since we have open circle at -4, we have to use open circle.
Domain = -4 < x < ∞
Between 1 to ∞, the graph is spreading over the y-axis.
Range = 1 ≤ y < ∞
By drawing the vertical line, that will intersect the curve at one point. So, it is a function.
Problem 4 :
Solution :
Between -2 to 2, the graph is spreading over the x-axis.
Domain = -2 ≤ x ≤ 2
Between 0 to 4, the graph is spreading over the y-axis.
Range = 0 ≤ y ≤ 4
By drawing the vertical line, that will intersect the curve at more than one point. So, it is not a function.
Problem 5 :
Solution :
Between -∞ to ∞, the graph is spreading over the x-axis.
Domain = All real numbers
Between -∞ to ∞, the graph is spreading over the y-axis.
Range = All real numbers
By drawing the vertical line, that will intersect the curve at one point. So, it is a function.
Problem 6 :
Solution :
Between -∞ to ∞, the graph is spreading over the x-axis.
Domain = All real numbers
Between -5 to ∞, the graph is spreading over the y-axis.
Range = -5 ≤ y ≤ ∞
By drawing the vertical line, that will intersect the curve at one point. So, it is a function.
Problem 6 :
Solution :
Between 0 to ∞, the graph is spreading over the x-axis.
Domain = 0 ≤ x ≤ ∞
Between -∞ to ∞, the graph is spreading over the y-axis.
Range = -∞ ≤ y ≤ ∞
By drawing the vertical line, that will intersect the curve at more than one point. So, it is not a function.
Problem 8 :
Solution :
Domain = All real values
Range = {1, 3}
For -1, we have two different outputs 1 and 3. So, it is not a function.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM