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Determine the domain and the range of the function.C. Determine where the function is increasing and where it is decreasing.

Determine the domain and the range of the function.C. Determine where the function-example-1

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Given:


f(x)=2x^2-x+1
a=2\text{ ; b= -1 ; c=1}

Graph opes upwards.

Let the vertex be (h,k)


h=-(b)/(2a)
h=-((-1))/(2(2))
h=(1)/(4)
k=f(h)
k=2((1)/(4))^2-(1)/(4)+1
k=2((1)/(16))-(1)/(4)+1
k=(1)/(8)-(1)/(4)+1
k=(1-2+8)/(8)
k=(7)/(8)
\text{Vertex}=((1)/(4),(7)/(8))

Axis of symmetry is


x=(1)/(4)

y- intercept

x=0,

y=1

There is no x intercept .

Domain:


(-\infty,\infty)

Range:


\lbrack(1)/(4),\infty)

The function is increasing:


((1)/(4),\infty)

The function is decreasing:


(-\infty,(1)/(4))

User Mehrdad Faraji
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