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GradeFunctions, Functions

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Which of the following is true regarding the symmetry of the function ? \[f(x) = x^{4}\ + x^{2}\ + 3\]

A. \[f(x)\ = f( - x)\]

B. \[f(x) = - f( - x)\]

C. It is an even function.

D. Symmetric wrt y axis

A. \[f(x)\ = f( - x)\]

B. \[f(x) = - f( - x)\]

C. It is an even function.

D. Symmetric wrt y axis

If \[f\left( x \right) = 4 - {x^2}\] and \[g\left( x \right) = 6x\] , which expression is equivalent to \[\left( {g - f} \right)\left( 3 \right)\] ?

Why does the vertical line test work?

If \[f:R \to R\] is given by $f\left( x \right)=\left\{ \begin{matrix}

1,\text{ if }x\text{ is rational} \\

0,\text{ if }x\text{ is irrational} \\

\end{matrix} \right.$, Then \[\left( {fof} \right)\left( {\sqrt 5 } \right) = \]

(A) \[1\]

(B) \[ - 1\]

(C) \[\sqrt 3 \]

(D) \[0\]

1,\text{ if }x\text{ is rational} \\

0,\text{ if }x\text{ is irrational} \\

\end{matrix} \right.$, Then \[\left( {fof} \right)\left( {\sqrt 5 } \right) = \]

(A) \[1\]

(B) \[ - 1\]

(C) \[\sqrt 3 \]

(D) \[0\]

If R denotes the set of all real number, then the function f: $R \to R$ defined by $f\left( x \right) = |x|\,\,is\,$

A. only one-one

B. only onto

C. both one-one and onto

D. neither one-one nor onto

A. only one-one

B. only onto

C. both one-one and onto

D. neither one-one nor onto

If \[f\left( x \right) = 4{x^2} + 3x + 7\]and \[g\left( x \right) = 3x - 5\] then find \[\left( {g \circ f} \right)\left( x \right)\]?

How do you find the domain and range of \[x + \sqrt {x - 1} \] ?

The following function is given as a set of ordered pairs \[\left\{ {\left( {1,3} \right),\left( {3, - 2} \right),\left( {0,2} \right),\left( {5,3} \right),\left( { - 5,4} \right)} \right\}\] what is the domain of this function?

How do you decide whether the relation \[xy = 9\] defines a function?

The function $f(x) = 10,000 - 1,500x$ can be used to predict the number of termites in an area $x$ days after the area has been treated. How many termites are predicted in the area after $5$ days?

Pens are shipped to the office supply store in boxes of $12$ each. Write a function rule to calculate the total number of pens when you know the number of boxes?

What is the domain of the derivative of \[\ln x\] ?

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