The graph of [tex]\mathbf{y = -x^5-x^4-x^3-x^2-x-1}[/tex] decreases as x approaches positive infinity and increases as x approaches negative infinity.
What is the domain of a polynomial function?
The domain of the polynomial function is the set of values for which the function appears real and is defined.
To find the correct pair that matches the tiles, we need to determine the x-intercepts and the y-intercepts of the polynomials. Then graph their coordinates on the graph.
The first polynomial function is:
[tex]\mathbf{y = -x^5-x^4-x^3-x^2-x-1}[/tex]
To find the y-intercepts, we set the values of x to be equal to zero
To find the x-intercepts, we set the values of y to be equal to zero
The graph of the polynomial function of the above point coordinate shows that:
- [tex]\mathbf{y = -x^5-x^4-x^3-x^2-x-1}[/tex] decreases as x approaches positive infinity and increases as x approaches negative infinity.
The second polynomial function is:
[tex]\mathbf{y = x^5+x^4+x^3+x^2+x+1}[/tex]
The graph of the polynomial function of the above point coordinate shows that:
- [tex]\mathbf{y = x^5+x^4+x^3+x^2+x+1}[/tex] increases as x approaches positive infinity and decreases as x approaches negative infinity.
The third polynomial function is:
[tex]\mathbf{y =-x^6+ x^5+x^4+x^3+x^2+x+1}[/tex]
- x-intercept = (-0.84,0)(1.9,0)
The graph of the polynomial function of the above point coordinate shows that:
- [tex]\mathbf{y =-x^6+ x^5+x^4+x^3+x^2+x+1}[/tex] decreases as x approach positive and negative infinity.
The fourth polynomial function is:
[tex]\mathbf{y =x^6+ x^5+x^4+x^3+x^2+x+1}[/tex]
The graph of the polynomial function of the above point coordinate shows that:
- [tex]\mathbf{y =x^6+ x^5+x^4+x^3+x^2+x+1}[/tex] increases as x approaches positive and negative infinity.
Learn more about the domain of a function here:
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