All categories

3 years ago

Analyze the key features of the graph f(x) = 1/x+3 -2

Mathematics

1 answer:

tia_tia [17]3 years ago

8 0

<h2>Explanation:</h2><h2></h2>

Here we have the following rational function:

$f(x) = \frac{1}{x+3} -2$

So the graph of this function is shown in the First Figure below. Let's define another function which is a parent function:

$g(x)=\frac{1}{x}$

Whose graph is shown in the second figure below. So we can get the graph of f from the graph of g this way:

Step 1. Shift the graph 3 units to the left:

$f_{1}(x) = \frac{1}{x+3}$

Step 2. Shift the graph 2 units down:

$f(x) = \frac{1}{x+3}-2$

Finally, the features of the graph of f are:

The graph of this function comes from the parent function g and the transformations are:

A shifting 3 units to the left

A shifting 2 units down

You might be interested in

H + 86.43 = 531.79<br><br> h = ___________

dedylja [7]

H= 445.36
because you bring the 86.43 over to the 531.79. which would make 86.43 a negative number. so you subtract 531.79 by 86.43

6 0

2 years ago

Read 2 more answers

Use a separate sheet of paper to solve the system of inequalities by graphing. Use the graph to decide if the point (1, –1) is i

Lena [83]

Answer:

The answer is no though, the point (1,-1) is below both.

Step-by-step explanation:

So the two inequalities are y≤-3x+3 and 3x+8y≥3

With inequalities you have to know a few things. First, when you graph you may have to use non solid lines. for instance, if you had x<5, 5 would not be part of the answer because it is only answers less than 5. so you represent this by making a dashed line that says "you cannot include values on this line". Second, with algebra, if you multiply both sides by a negative it flips the inequality. for instance -y > 54 you would multiply (or divide) by -1 and it would change to y < -54. Third, when graphing an inequality, treat it like an equation and graph the line as if it were said equation(with solid or dashed lines as needed) then, if it is y > f(x) you shade in the section above the line and y < f(x) shades in below. The shaded part is your answer basically. Now lets get into yours.

y≤-3x+3

It is already in the form y = f(x) so grapht he line 3x + 3 with a solid line since it is y is less than or equal to, then shade below that line.

3x+8y≥3

First get it so y is by itself

3x+8y≥3

8y≥3 - 3x

y ≥ 3/8 - 3/8 x

Now grapht his line with a solid line and shade the area above it.

Now, the shaded area below between y ≥ 3/8 - 3/8 x and y≤-3x+3 and the lines are your answer, so you need to check if the point (1, -1) is in this shared shaded area or on one of the lines.

The answer is no though, the point (1,-1) is below both.

6 0

3 years ago

What will be the answer if we multiply a+b by ab

VARVARA [1.3K]

Step-by-step explanation:

(a+b)(ab)

${a}^{2} b + a {b}^{2}$

6 0

2 years ago

PLEASE HELP (30 POINTS) Solve the rational equation x/3 = x^2/x + 5 , and check for extraneous solutions.

anygoal [31]

Option C: $x=0$ and $x=\frac{5}{2}$ are the solutions.

Explanation:

The equation is $\frac{x}{3} =\frac{x^{2} }{x+5}$

We shall determine the value of x, by simplifying the equation.

$\begin{aligned} x(x+5) &=3 x^{2} \\ x^{2}+5 x &=3 x^{2} \\ 2 x^{2}-5 x &=0 \\ x(2 x-5) &=0 \end{aligned}$

Thus, $x=0$ and $x=\frac{5}{2}$ are the solutions.

Now, let us check whether the solutions are extraneous solutions.

Let us substitute $x=0$ in the original equation to check whether both sides of the equation are equal.

$\begin{aligned}&\frac{0}{3}=\frac{0^{2}}{0+5}\\&0=\frac{0}{5}\\&0=0\end{aligned}$

Thus, both sides of the equation are equal.

Hence $x=0$ is a true solution.

Now, Let us substitute $x=\frac{5}{2}$ in the original equation to check whether both sides of the equation are equal.

$\begin{aligned}\frac{\left(\frac{5}{2}\right)}{3} &=\frac{\left(\frac{5}{2}\right)^{2}}{\left(\frac{5}{2}\right)+5} \\\frac{5}{6} &=\frac{\left(\frac{25}{4}\right)}{\left(\frac{15}{2}\right)} \\\frac{5}{6} &=\frac{5}{6}\end{aligned}$

Thus, both sides of the equation are equal.

Hence, $x=\frac{5}{2}$ is a true solution.

Thus, solutions are not extraneous.

Hence, Option C is the correct answer.

8 0

3 years ago

PLEASE HELP ME

MA_775_DIABLO [31]

Mean: $620, Mode: $600

Let's sort the rank stats.

First quartile: $580

Median: $610

Third quartile: $645

85th percentile: $685

OK, we're ready. What happened to a and b?

c. $645 is the third quartile, 75th percentile. That means 25% of the salaries are higher.

Answer: 25%

d. $685 is the 85th percentile, 15% greater.

Answer: 15%

e. The mean is the sum of all the salaries divided by the count.

Mean = Sum / Count

So the sum is the count times the mean,

Sum = Count × Mean = 100 × $620 = $62,000

Big payroll.

Answer: $62,000

4 0

3 years ago