# Use long division to rewrite the equation for g in the formtext{quotient}+frac{remainder}{divisor}Then use this form of the function's equation and

Question
Transformations of functions

Use long division to rewrite the equation for g in the form
$$\text{quotient}+\frac{remainder}{divisor}$$
Then use this form of the function's equation and transformations of
$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}}}}$$
to graph g.
$$\displaystyle{g{{\left({x}\right)}}}={\frac{{{2}{x}+{7}}}{{{x}+{3}}}}$$

2020-12-22

Step 1
$$\displaystyle{g{{\left({x}\right)}}}={\frac{{{2}{x}\ +\ {7}}}{{{\left\lbrace{x}\ +\ {3}\right\rbrace}}}}$$
$$\begin{array} & 2 & \\ \hline \underline{x\ +\ 3|} & 2x & +7 \\ & \ominus2x & \ominus+6 \\ \hline & & 1 \end{array}$$
The quotient is 2 and the remainder is $$\displaystyle{\frac{{{1}}}{{{x}\ +\ {3}}}}$$
$$\displaystyle{g{{\left({x}\right)}}}={2}\ +\ {\frac{{{1}}}{{{x}\ +\ {3}}}}$$ We can graph g by horizontal shifting f 3 units left then vertical shifting 2 units up
Step 2

### Relevant Questions

Use long division to rewrite the equation for g in the form
$$\text{quotient}+\frac{remainder}{divisor}$$
Then use this form of the function's equation and transformations of
$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}}}}$$
to graph g.
$$\displaystyle{g{{\left({x}\right)}}}={\frac{{{3}{x}-{7}}}{{{x}-{2}}}}$$

Let B be a $$(4\times3)(4\times3)$$ matrix in reduced echelon form.

a) If B has three nonzero rows, then determine the form of B.

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The coefficient matrix for a system of linear differential equations of the form $$y^1=Ay$$  has the given eigenvalues and eigenspace bases. Find the general solution for the system

$$\lambda1=3\Rightarrow \begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix}$$

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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).
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Let $$A = (1, 1, 1, 0), B = (-1, 0, 1, 1,), C = (3, 2, -1, 1)$$
and let $$D = \{Q \in R^{4} | Q \perp A, Q \perp B, Q \perp C\}$$.
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$$|y+7|\geq 1$$
$$y\leq -7\ or\ y \leq -8$$
$$y\geq -7\ or\ y \leq -8$$
$$y\geq -7\ or\ y \leq -8$$
$$y\geq -7$$
$$y\leq -8$$