Question
Determine whether the following functions are linear or non-linear and explain how you know.
Hint:
In simpler terms, a linear function is one whose graph is a straight line when plotted on the xy plane, whereas a non- linear function can be any curve in the xy plane. So we will make a table of different values of x and corresponding values of y and plot the ordered pairs in the xy plane to get a graph.
The correct answer is: greater than 1
Step by step solution:
The given equation is
First we make a table of points satisfying the equation.
Putting x = 0 in the above equation, we will get, y = 4
Similarly, putting x = 1, in the above equation, we get y = 5
Continuing this way, we have
For x = 2, we get y = 7
For x = 3, we get y = 11
For x = 4, we get y = 19
Making a table of all these points, we have
X
0
1
2
3
4
Y
4
5
7
11
19
Now we plot these points on the graph.
We join these points with a smooth curve to get the curve
We can clearly see that the graph is not a straight line.
Hence, the given function is not linear.
Making a table of all these points, we have
There are other ways to determine if a given equation is linear or not. If an equation can be written in the form y = ax + b, where a and b are constants, then the function is linear. Another way to check if an equation is linear is by checking the highest degree of a term in the equation. If the highest degree of any term in the equation is 1, then the equation is linear, and if the degree of any term is greater than 1, then the equation is non-linear.
Related Questions to study
Determine whether the following functions are linear or non-linear and explain how you know.
There are other ways to determine if a given equation is linear or not. If an equation can be written in the form y = ax + b, where a and b are constants, then the function is linear. Also, the graph of a linear equation is always a straight line. So, we can plot a graph of the given equation and check if it is a straight line.
Determine whether the following functions are linear or non-linear and explain how you know.
There are other ways to determine if a given equation is linear or not. If an equation can be written in the form y = ax + b, where a and b are constants, then the function is linear. Also, the graph of a linear equation is always a straight line. So, we can plot a graph of the given equation and check if it is a straight line.
Choose the synonym for ‘Revision’.
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,,,….
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Explain why it would be beneficial to choose the inputs -8, -4, 0 , 4, and 8 for the function
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Explain why it would be beneficial to choose the inputs -8, -4, 0 , 4, and 8 for the function
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Make and test a conjecture about the sum of numbers from 1 to 7. Write a conjecture for the general case.
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Make a sentence using the word 'dreadful'
Graph the following functions by filling out the X/Y chart using the given inputs
| X | -7 | -6 | -3 | 2 | 9 |
| Y |
We can find the tabular values for any points of x and then plot them on the graph. But we usually choose values for which calculating y is easier. Either way, we need points satisfying the equation to plot its graph.
Graph the following functions by filling out the X/Y chart using the given inputs
| X | -7 | -6 | -3 | 2 | 9 |
| Y |
We can find the tabular values for any points of x and then plot them on the graph. But we usually choose values for which calculating y is easier. Either way, we need points satisfying the equation to plot its graph.
Make and test a conjecture about the square of even numbers.
Make and test a conjecture about the square of even numbers.
Graph the following functions by filling out the X/Y chart using the given inputs
| X | -9 | -8 | -5 | 0 | 7 |
| Y |
We can find the tabular values for any points of x and then plot them on the graph. But we usually choose values for which calculating y is easier. Either way, we need points satisfying the equation to plot its graph.
Graph the following functions by filling out the X/Y chart using the given inputs
| X | -9 | -8 | -5 | 0 | 7 |
| Y |
We can find the tabular values for any points of x and then plot them on the graph. But we usually choose values for which calculating y is easier. Either way, we need points satisfying the equation to plot its graph.
