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3 years ago

Graph the piecewise-defined function

Mathematics

2 answers:

astraxan [27]3 years ago

3 0

Start by graphing y = |x|. Its vertex is at (0,0), and the graph opens up.

Now translate the entire graph 4 units up. The new vertex will be at (0,4). Draw an empty circle around this point.

Darken the graph of y = |x|+4 ONLY for the part which is left of the y-axis.

Now plot a dark dot at (0,4). Draw a dark, horiz. line from that dot to the right.

That's it!

STatiana [176]3 years ago

3 0

<h2>Answer with explanation:</h2>

The function f(x) is given by:

f(x)= |x|+4, if x<0

and 4 , if x ≤ 0.

for x<0

The graph of the function is a strictly decreasing continuous graph i.e. a line with a slope as: -1.

Since, the function f(x) for x<0 is given by:

f(x)= -x+4

also at x=0- f(x)=4

Also , for x≥0 the graph of the function is a straight line parallel to the x-axis.

Also, the left hand limit at x=0 is equal to the right hand limit at x=0 is equal to the function's value at x=0.

Hence, the graph of the function is continuous for all the real values.

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Gwar [14]

Answer: 47

Step-by-step explanation: To solve this problem, let's use t to represent our tens digit and u to represent our units digit so that the value of our number can be represented as 10t + u.

If we represent the value of our number as 10t + u, the value of the number with the digits reversed can be represented as 10u + t.

Since the first sentence states that the sum of the digits of a two-digit number is 11, that's t + u = 11.

Reading through our second sentence, when the digits are reversed, the new number is 27 more than the original number, that's 10u + t "is" which means equals 27 more than the original number that's 10t + u + 27.

So 10t + u = 10t + u + 27.

Before solving this system however, let's rearrange our second equation so that the t's and u's are on the same side by subtracting 10t and u from both sides to get 9u - 9t = 27 and when we rewrite our first equation above it, instead of writing it as t + u = 11, let's write it as t + u = 11 so that our u's and t's will match up in the system.

To solve this system, let's use addition so multiply the top equation by 9 to get 9u + 9t = 99 and 9u - 9t = 27 so that when we add the equations together the t's cancel and we get 18u = 126. Dividing both sided by 18, u = 7.

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Since our tens digit is 4 and our units is 7, our number must be 47.

I have also attached my work on a whiteboard.

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Serhud [2]

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Step-by-step explanation:

In order to calculate the daily intake of sodium we first need to calculate the mass of sodium present in both snacks, this is given by their sum.

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We can now apply a rule of three for which the total sodium from the snacks is related to 66.4% in the same proportion as "x" mg, which is the value we want to know, is related to 100%. So we have:

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