I need help! <br> f(x)=-3x+6/4x-8

state domain and range, intercepts, relative max and relative mins points and values, intervals of increase and decrease, interv

Aloiza [94]

The domain of the graph is -∝ < x < ∝ and the range of the graph is y > -2. Also, the symmetry is x = -3

<h3>The domain and range of the graph</h3>

From the graph, we can see that the x values extend indefinitely

So, the domain of the graph is -∝ < x < ∝

However, the minimum y value is -2 and it increases from there

So, the range of the graph is y > -2

<h3>The intercepts</h3>

This is where the graph crosses the axes

So, we have the intercepts to be

x-intercept = -1 and -5
y-intercept = 1

<h3>Relative max and relative mins points and values, </h3>

The graph has no relative maximum and the relative minimum is (-3, 2)

<h3>Intervals of increase and decrease</h3>

There are the intervals where the function increases and decreases

So, we have the intervals to be

Increasing interval: (-3, ∝)
Decreasing interval: (-∝, -3)

<h3>Intervals of positive and negative</h3>

There are the intervals where the function is positive and negative

So, we have the intervals to be

Positive interval: (-∝, -5) and (1, ∝)
Negative interval: (-5, -1)

<h3>The symmetry</h3>

This is the line that divides the graph equal part

In this case, the symmetry is x = -3

<h3>The end behavior</h3>

Using the intervals where the function is positive and negative, the end behavior is

As x ⇒ ∝, f(x) ⇒ +∝
As x ⇒ -∝, f(x) ⇒ -∝

Read more about functions at:

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8 0

2 years ago

What is 6 with a 30% increase

zhannawk [14.2K]

Answer:

70 increased by 6 percent = 74.2

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

What is the relative minimum of f(x)= -x2-4x+6

matrenka [14]

Answer:

(−2,10)

Step-by-step explanation:

hope this helps

3 0

3 years ago

Find the equation of the line that passes through (0, -3) and is parallel to

Tresset [83]

Hey there!

$\\$

Answer:

$\green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}$

$\\$

Explanation:

To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.

Let the line that we are trying to determine its equation be $\: \sf{d_1} \:$ and the line that is parallel to $\: \sf{d_1} \:$ be $\: \sf{d_2} \:$ .

$\sf{d_2} \:$ passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:

$\sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}}$

$\\$

⇒Subtitute the values :

$\sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )}$

$\implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}$

$\sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}}$ .

Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:

Slope-Intercept Form:

$\sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \: the \: line \: and \: b \: is \: the \: y-intercept.}$

$\implies \sf{y = \bold{\dfrac{7}{6}}x + b}$ $\\$

We know that the coordinates of the point (0 , -3) verify the equation since it is on the line $\: \sf{d_1} \:$ . Now, replace y with -3 and x with 0:

$\implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Therefore, the equation of the line $\: \bold{d_1} \:$ is $\green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}$

$\\$

▪️Learn more about finding the equation of a line that is parallel to another one here:

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8 0

1 year ago

Read 2 more answers

Is point (2,1) on the the line represented by the equation x+2y=5

Sphinxa [80]

To check if this point lies on the line, plug in a 2 for x and a y for 1 and solve

x+2y=5
2+2(1)=5
4=5

Since this statement isn't true, then the point doesn't lie on the line

Hope this helps

6 0

3 years ago

Read 2 more answers

I need help! f(x)=-3x+6/4x-8