Select the equation in which the slope equals -9 and the y-intercept equals 3.

If the function f (x) has a domain of (a,b] and a range of [c,d), then what is the domain and range of g (x) = m × f (x) + n?

xz_007 [3.2K]

<h3>Answer: Choice A</h3>

Domain = (a,b]

Range = [mc + n,md + n)

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Explanation:

The domain stays the same because we still have to go through f(x) as our first hurdle in order to get g(x).

Think of it like having 2 doors. The first door is f(x) and the second is g(x). The fact g(x) is dependent on f(x) means that whatever input restrictions are on f, also apply on g as well. So going back to the "2 doors" example, we could have a problem like trying to move a piece of furniture through them and we'd have to be concerned about the f(x) door.

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The range will be different however. The smallest value in the range of f(x) is y = c as it is the left endpoint. So the smallest f(x) can be is c. This means the smallest g(x) can be is...

g(x) = m*f(x) + n

g(x) = m*c + n

All we're doing is replacing f with c.

So that means mc+n is the starting point of the range for g(x).

The ending point of the range is md+n for similar reasons. Instead of 'c', we're dealing with 'd' this time. The curved parenthesis says we don't actually include this value in the range. A square bracket means include that value.

6 0

2 years ago

What is the value of the expression below when y = 3? 10y - 8

ycow [4]

Answer:

Step-by-step explanation:

<h3>Given, y = 3 </h3>

substitute this value in given expression

=> 10y - 8

=> 10(3) - 8

=> 30 - 8

=> 22...ans

<h2>HOPE IT HELPS U!!!!</h2>

3 0

2 years ago

alfredo bought a fishing pole for 60 off it's original price of $97 if the tax was 4% how much did alfredo pay for the fishing p

Agata [3.3K]

Answer:

$40.4

Step-by-step explanation:

The regular price of the fishing rod is $97

There is a 60% discount from that price.

The discount is equal to 60% of $97 which is equal to .60 * $97 which is equal to $58.2

Discount is like a markdown, so subtract $58.2 from the price of the item before the change to get $97 - $58.2 = $38.8

This is the price of the item before tax is applied.

Now you apply the sales tax of 4%.

4% of $38.8 is equal to .04 * $38.8 which is equal to $1.552

Tax is like a markup, so add $1.552 to the price of the item before tax was applied to get a selling price of $38.8 + $1.552 which is equal to $40.352

Round it up and the answer is $40.4

3 0

3 years ago

1. The scale of a map is 1:1000. What are the actual dimensions of a

kakasveta [241]

Answer:

Step-by-step explanation:

4 cm × 1000 = 4000 cm = 40 meters

3 cm × 1000 = 3000 cm = 30 meters

A 4 cm by 3 cm section on the map represents 40 m by 30 m.

area = 40 m × 30 m = 1200 m²

6 0

2 years ago

Graph the function. Upload a handwritten copy of your graph as your final answer.

Serhud [2]

The function is divided in 2 parts:

For x<0, the function is $y=x$ , which is a linear function, and its graph is a line.

For x≥0, the function is $y=-x^2$ , which is a quadratic function, and its graph is a parabola.

Note that y=x is the line containing the points (0, 0), (1, 1), (5, 5) etc, that is, it is the line passing through the origin, with an inclination of 45° with the positive x-axis.

The parabola $y=-x^2$ is the parabola $y=x^2$ reflected with respect to the x-axis. It contains points like (0, 0), (-1, 1), (2, -4) etc...

The 2 graphs, with domain all real numbers, are shown in the first picture.

The second picture is the graph of the function described in our problem. We use the first picture, but restrict the domains.

That is, we delete the part of the line corresponding to x≥0, and the part of the parabola corresponding to x<0.

7 0

3 years ago