Sketch a graph of the function. Use transformations of functions whenever possible. f(x)=2x^{2} - 1

Determine whether each of the given sets is a real linear space, if addition and multiplication by real scalars are defined in the usual way. For those that are not, tell which axioms fail to hold. The function are real-valued. All rational functions f/g, with the degree off ≤≤ the degree ofg (including f = 0).

g is related to one of the parent functions described in Section 1.6. Describe the sequence of transformations from f to g. g(x) = 2 ||x + 5||

For each of the following functions f (x) and g(x), express g(x) in the form a: f (x + b) + c for some values a,b and c, and hence describe a sequence of horizontal and vertical transformations which map f(x) to g(x).
${\displaystyle f\left(x\right)=x^2-2,g\left(x\right)=2+8x-4x^2}$

Sketch a graph of the function. Use transformations of functions whenever possible. ${\displaystyle f\left(x\right)=-{(x-1)}^4}$

If ${\displaystyle f\left(x\right)=x^2-2x+3}$ how do you find f(a+h)-f(a)/h?

Sketch a graph of the function. Use transformations of functions when ever possible. ${\displaystyle f\left(x\right)=\sqrt{3}\{-x\}}$

Sketch a graph of the function. Use transformations of functions whenever possible. ${\displaystyle f\left(x\right)=3x^2}$