1. Graph each equation. Tell whether the equation represents a function.
a. y = (x - 2)^2 - 1
b. x + y = 6
c. y = |x| -3
d. y = x^2 + 1
How am I supposed to graph these?
2. For each function, determine whether the given points are on the graph.
a. y = 7x - 2; (1, 5) and (2, 10)
Can anyone help me?
make a table of values for each, plot the points and join them with smooth curves for the 1st and last.
The 1st and last are parabolas, the first has a vertex at (2,-1), the last one has a vertex at (0,1)
Both open up
the other two are linear , that is, straight lines, but
the y = |x| -3 lies all above the x-axis
I suggest graphing y = x , then reflecting the part which falls below the x-axis in the x-axis then moving the curve down by 3 units
see:
http://www.wolframalpha.com/input/?i=plot+y+%3D+%7Cx%7C+-+3
One of my favourite webpages, simply change the equation for the others.
The line
" the y = |x| - 3 lies all above the x-axis" is not correct,
should have said
"the y = |x| - 3 lies all above -3 "
To graph each equation, you can follow these steps:
1. Start by setting up a coordinate plane with the x and y axes.
2. For each equation, choose a range of x-values to plot on the graph. This will depend on the specific equation and the desired extent of the graph.
3. Plug in different x-values into the equation to find the corresponding y-values. You can choose multiple x-values to get a range of points that form the graph.
4. Plot the resulting points on the graph by matching each x-value with its corresponding y-value.
5. Once you have plotted enough points, connect them to form a curve or a line, depending on the shape of the graph.
Let's go through each equation and determine if it represents a function:
a. y = (x - 2)^2 - 1:
To graph this equation:
1. Choose a range of x-values, such as [-5, 5].
2. Plug in different x-values into the equation to find the corresponding y-values. For example, if we choose x = -2, we have y = (-2 - 2)^2 - 1 = 1. So, one point is (-2, 1).
3. Repeat this process for additional x-values.
4. Plot the points on the graph and connect them to form the curve.
Since every x-value has only one corresponding y-value, this equation represents a function.
b. x + y = 6:
To graph this equation:
1. Choose a range of x-values, such as [-5, 5].
2. Rearrange the equation to solve for y: y = 6 - x.
3. Plug in different x-values into the equation to find the corresponding y-values. For example, if we choose x = 2, we have y = 6 - 2 = 4. So, one point is (2, 4).
4. Repeat this process for additional x-values.
5. Plot the points on the graph and connect them to form a line.
Since one x-value can have multiple corresponding y-values, this equation does not represent a function.
c. y = |x| - 3:
To graph this equation:
1. Choose a range of x-values, such as [-5, 5].
2. Plug in different x-values into the equation to find the corresponding y-values. For example, if we choose x = -3, we have y = |-3| - 3 = 3 - 3 = 0. So, one point is (-3, 0). Another point could be (3, 0).
3. Repeat this process for additional x-values.
4. Plot the points on the graph and connect them to form a "V" shape with the vertex at (0, -3).
Since every x-value can have multiple corresponding y-values and the graph is not a straight line, this equation does not represent a function.
d. y = x^2 + 1:
To graph this equation:
1. Choose a range of x-values, such as [-5, 5].
2. Plug in different x-values into the equation to find the corresponding y-values. For example, if we choose x = -2, we have y = (-2)^2 + 1 = 4 + 1 = 5. So, one point is (-2, 5).
3. Repeat this process for additional x-values.
4. Plot the points on the graph and connect them to form a curve.
Since every x-value has only one corresponding y-value, this equation represents a function.
Now, let's move to the second question.
2. For each function, determine whether the given points are on the graph.
a. y = 7x - 2; (1, 5) and (2, 10):
To check if the given points are on the graph, simply plug in the x-coordinate of each point into the equation and see if the resulting y-coordinate matches.
For the point (1, 5):
Plugging in x = 1 into the equation y = 7x - 2, we get y = 7(1) - 2 = 7 - 2 = 5. The y-coordinate matches, so the point (1, 5) is on the graph.
For the point (2, 10):
Plugging in x = 2 into the equation y = 7x - 2, we get y = 7(2) - 2 = 14 - 2 = 12. The y-coordinate does not match, so the point (2, 10) is not on the graph.
Therefore, only the point (1, 5) is on the graph of y = 7x - 2.