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AleksandrR [38]
2 years ago
5

Sketch the graph of the function f(x) = x + |x|.

Mathematics
1 answer:
masha68 [24]2 years ago
5 0

Answer:

The absolute value can be graphed using the points around the vertex (0, 0), (-2, 0), (-1, 0), (1, 2), (2, 4).

Step-by-step explanation:

To find the x coordinate of the vertex, set the inside of the absolute value x equal to 0. In this case, x = 0.

Replace the variable x with 0 in the expression.

y = (0) + |0|

PS: The absolute value is the distance between a number and zero. The distance between 0 and 0 is 0.

y = 0 + 0

y = 0

The absolute value vertex is (0, 0).

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation: (-∞, ∞)

Set-Builder Notation: {x|x ∈R}

For each x value, there is one y value. Select few x from the domain. It would be more useful to select the values so that they are around the x value of the absolute value vertex.

Substitute the x value -2 into f(x) = x + |x|. In this case, the point is (-2, 0).

y = 0

Substitute the x value 1 into f(x) = x + |x|. In this case, the point is (1, 2).

y = 2

Substitute the x value 2 into f(x) = x + |x|. In this case, the point is (2, 4).

y = 4

You can find the graph in the attachment.

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2 years ago
Write an equation in point-slope form for the line that has a slope of 4/5 and contains the point (−5, −3).
ankoles [38]

y = mx + b, where m = slope, and b = y-intercept.

Since you are not given the y-intercept, you have to solve for it through the equation, y = (4/5)x (which is the slope you are given) + b, and replace x and y with values given, which are (-5,-3)

y = (4/5)x + b

-3 = (4/5)(-5) + b

-3 = -4 + b

1 = b


Then replace b in the first equation to get the answer

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3 years ago
If light travels 6.71 x 108 miles in one hour, how many miles will it travel in 90 minutes?
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2 years ago
A student placement center has requests from five students for interviews regarding employment with a particular consulting firm
bagirrra123 [75]

Answer: a) 1 / 10

b) 3 / 10

c) 1 / 5

d) 3 / 5

Step-by-step explanation:

Total number of requests five students for interviews regarding employment with the consulting firm = 5

Number of students that are maths majors = 3

Probability of selecting a maths student is 3 / 5

Number of students that are statistics majors = 2

Probability of selecting a statistics student is 2 / 5

a) the probability that both selected students are statistics majors

= 2 / 5 × 1 / 4 = 2 / 20 = 1 / 10

b) the probability that both students are math majors

= 3 / 5 × 2 / 4 = 6 / 20 = 3 / 10

c) the probability that at least one of the students selected is a statistics major will be p( one statistics and the other, maths) + p( one maths and the other, statistic) - p( both are mathematics)

= (2 / 5 × 1 / 4 ) + ( 2 / 5 × 3 / 4 ) - (3 / 5 × 2 / 4)

= 2 / 10 + 6 / 20 - 6 / 20

= 1 / 5 + 3 / 10 - 3 / 10

= 1 / 5

d) the probability that the selected students have different majors is p(one is maths and the other is statistics) + p(one is statistics and the other is maths)

(3 / 5 × 2 / 4) + (2 /5 × 3 / 4)

= 6 / 20 + 6 / 20 = 12 / 20

= 3 / 5

3 0
3 years ago
*The difference between a number and 8 is greater than 2.
scoray [572]

Answer:

the answer is 5

Step-by-step explanation:

6 0
3 years ago
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