Graph the folowing. State the parent function, transformations, domain and range.

shelbs624c
2021-11-18
Answered

Graph the folowing. State the parent function, transformations, domain and range.

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Michele Grimsley

Answered 2021-11-19
Author has **19** answers

Step 1

Given function is, f(x)=x+2

The graph of f(x) is as shown below :

Step 2

Parent function : x

Transformations : Vertical shift of +2 or Left shift by 2

Domain, D :$(-\mathrm{\infty},\mathrm{\infty})$

Range, R :$(-\mathrm{\infty},\mathrm{\infty})$

Given function is, f(x)=x+2

The graph of f(x) is as shown below :

Step 2

Parent function : x

Transformations : Vertical shift of +2 or Left shift by 2

Domain, D :

Range, R :

asked 2022-07-19

Can asymptotes be curved?

When I was first introduced to the idea of an asymptote, I was taught about horizontal asymptotes (of form y=a) and vertical ones ( of form x=b).

I was then shown oblique asymptotes-- slanted asymptotes which are not constant (of the form y=ax+b).

What happens, though, if we've got a function such as

$f(x)={e}^{x}+\frac{1}{x}?$

Is $y={e}^{x}$ considered an asymptote in this example?

Another example, just to show you where I'm coming from, is

$g(x)={x}^{2}+\mathrm{sin}(x)$

-- is $y={x}^{2}$ an asymptote in this case?

The reason that I ask is that I don't really see the point in defining oblique asymptotes and not curved ones; surely, if we want to know the behaviour of y as $x\to \mathrm{\infty}$, we should include all types of functions as asymptotes.

If asymptotes cannot be curves, then why arbitrarily restrict asymptotes to lines?

When I was first introduced to the idea of an asymptote, I was taught about horizontal asymptotes (of form y=a) and vertical ones ( of form x=b).

I was then shown oblique asymptotes-- slanted asymptotes which are not constant (of the form y=ax+b).

What happens, though, if we've got a function such as

$f(x)={e}^{x}+\frac{1}{x}?$

Is $y={e}^{x}$ considered an asymptote in this example?

Another example, just to show you where I'm coming from, is

$g(x)={x}^{2}+\mathrm{sin}(x)$

-- is $y={x}^{2}$ an asymptote in this case?

The reason that I ask is that I don't really see the point in defining oblique asymptotes and not curved ones; surely, if we want to know the behaviour of y as $x\to \mathrm{\infty}$, we should include all types of functions as asymptotes.

If asymptotes cannot be curves, then why arbitrarily restrict asymptotes to lines?

asked 2022-06-11

What is the distance between the following polar coordinates?:

$(11,\frac{17\pi}{12}),(4,\frac{\pi}{8})$

$(11,\frac{17\pi}{12}),(4,\frac{\pi}{8})$

asked 2021-02-19

Trigonometric integral Evaluate the following integrals.

$\int {\mathrm{sin}}^{2}0{\mathrm{cos}}^{5}0d0$

asked 2022-06-13

From a proof of Simpson's rule using Taylor polynomial where $f\in [{x}_{0},{x}_{2}]$ and, for

${x}_{1}={x}_{0}+h$

where

$h=\frac{{x}_{2}-{x}_{0}}{2}$

it got:

${\int}_{{x}_{0}}^{{x}_{2}}f(x)dx\cong 2hf({x}_{1})+{h}^{3}\frac{{f}^{\u2033}({x}_{1})}{3}+{h}^{5}\frac{{f}^{(4)}(\xi )}{60}$

and then, it changed ${f}^{\u2033}({x}_{1})$ by

$\frac{f({x}_{0})-2f({x}_{1})+f({x}_{2})}{{h}^{2}}$

Where it came?

${x}_{1}={x}_{0}+h$

where

$h=\frac{{x}_{2}-{x}_{0}}{2}$

it got:

${\int}_{{x}_{0}}^{{x}_{2}}f(x)dx\cong 2hf({x}_{1})+{h}^{3}\frac{{f}^{\u2033}({x}_{1})}{3}+{h}^{5}\frac{{f}^{(4)}(\xi )}{60}$

and then, it changed ${f}^{\u2033}({x}_{1})$ by

$\frac{f({x}_{0})-2f({x}_{1})+f({x}_{2})}{{h}^{2}}$

Where it came?

asked 2021-11-20

Write the integral in terms of u and du. Then evaluate: $\int {(x+25)}^{-2}dx,u=x+25$

asked 2021-05-09

Find all rational zeros of the polynomial, and write the polynomial in factored form.

$P\left(x\right)=4{x}^{3}-7x+3$

asked 2022-04-10

Compute $\int {e}^{t}\ufeff\sqrt{9{e}^{2t}+4}dt$.