Which set of ordered pairs does not represent a function?
1 answer:
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Answer:
Domain: All Real numbers
CoDomain : All Real numbers
Range: ; that is: Real numbers larger than or equal to zero
Step-by-step explanation:
Notice that the graphed function can use any Real number x (from - infinity to + infinity) and produce an output. Therefore, the Domain of the function plotted in graph 3 is : All Real numbers.
The set of possible outputs (CoDomain) is also the set of all Real numbers (notice that the y-axis extends form - infinity to + infinity
But the Range (the actual set of the collection of outputs of the function) is just a subset of the CoDomain consisting of the Real numbers larger than or equal to zero (notice that the drawing of the function touches the x axis and lies completely on the upper half of the plane.
The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is
and
We have given that,
f(x) = 2x^2 + x + 4
x g(x)
-2 1
-1 3
0 5
1 7
2 9
<h3>What is a polynomial function?</h3>A polynomial function is a relation where a dependent variable is equal to a polynomial expression.
A polynomial expression is an expression including numbers and variables, where variables are raised to non-negative powers.
The general form of a polynomial expression is:
a₀ + a₁x + a₂x² + a₃x³ + ... + anxⁿ.
The highest power to a variable is the degree of the polynomial expression. When degree = 2, the function is a quadratic function.
When degree = 1, the function is a linear function.
<h3>How do we solve the given question?</h3>
The quadratic function is given to us:f(x) = 2x^2 + x + 4.
We need to determine the linear equation g(x).
Since it's a linear equation we use the two-point method to determine the equation.
<h3>What is the two-point?</h3>y-y₁ = ((y₂-y₁)/(x₂-x₁))*(x-x₁)
We take the points g(-2) =1, g(-1) = 3
g(x) - g(1) = ((g(-2)-g(-1))/(-2+1))*(x-1)or,
g(x) - 1 = ((-2-(-1))/(-2+1))*(x-1)or, g(x) - 1 = -1(-x+1)or,
g(x) = x - 1 + 1 = x
∴ g(x) = x , is the linear function g(x)
We are asked to find the solution to the system of equations f(x) and g(x).To find the solution we need to check what is the common solution to both f(x) and g(x).
For that, we equate f(x) and g(x).2x^2 + x + 4 = x or, 2x² - x +x- 4 = 0or, 2x^2 - 4 = 02(x^2-2)=0x^2-2=0g(-1) = 3(from the table)
The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is and
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