Question
Determine whether the following functions are linear or non-linear and explain how you know.
![straight Y equals straight x cubed minus straight x squared](data:image/png;base64,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)
Hint:
To check if a function is linear, we check the highest degree of a term in the equation. If the highest degree of all the terms in the equation is 1, then the equation is linear, and if the degree of any terms is greater than 1, then the equation is non-linear. We check the degree of each of the terms in the given equation to check if the equation is linear.
The correct answer is: greater than 1
Step by step solution:
The given equation is
![straight Y equals straight x cubed minus straight x squared](data:image/png;base64,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)
We check the degree of each of the terms in the above equation.
The degree of a term is the sum of the exponents of all the variables that are present in the term. Here, the only variables are x and y.
In the left hand side, we have y.
Clearly, degree of this term = 1
In the right hand side, the first term we have is x3
Degree of this term = 3
Thus, the degree of one of the terms in the equation is greater than 1.
Hence, the function is not linear.
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.
Related Questions to study
Choose the synonym for ‘Revision’.
Choose the synonym for ‘Revision’.
Determine whether the following functions are linear or non-linear and explain how you know.
![Y equals x squared minus 2 x](data:image/png;base64,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)
Determine whether the following functions are linear or non-linear and explain how you know.
![Y equals x squared minus 2 x](data:image/png;base64,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)
Select the correct verb.
Select the correct verb.
Describe the pattern in the numbers. Write the next number in the pattern. 1
,,,….
Describe the pattern in the numbers. Write the next number in the pattern. 1
,,,….
Make and test a conjecture about the sum of two even numbers.
Make and test a conjecture about the sum of two even numbers.
Explain why it would be beneficial to choose the inputs -8, -4, 0 , 4, and 8 for the function
![straight Y equals fraction numerator 3 x over denominator 4 end fraction minus 2](data:image/png;base64,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)
Integral values means the value of an integer, that is, the value should be number, either positive or negative. The above method of choosing x in such a way that there is no fraction or square root left is a very important trick required while making a graph of the equation.
Explain why it would be beneficial to choose the inputs -8, -4, 0 , 4, and 8 for the function
![straight Y equals fraction numerator 3 x over denominator 4 end fraction minus 2](data:image/png;base64,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)
Integral values means the value of an integer, that is, the value should be number, either positive or negative. The above method of choosing x in such a way that there is no fraction or square root left is a very important trick required while making a graph of the equation.
Make and test a conjecture about the sum of numbers from 1 to 7. Write a conjecture for the general case.
Make and test a conjecture about the sum of numbers from 1 to 7. Write a conjecture for the general case.
Choose the correct synonym for "Prediction"
Choose the correct synonym for "Prediction"
Make a sentence using the word 'dreadful'
Make a sentence using the word 'dreadful'
Graph the following functions by filling out the X/Y chart using the given inputs
![Y equals square root of X plus 7 end root](data:image/png;base64,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)
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
![Y equals square root of X plus 7 end root](data:image/png;base64,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)
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
![straight Y equals square root of X plus 9 end root](data:image/png;base64,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)
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
![straight Y equals square root of X plus 9 end root](data:image/png;base64,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)
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.