Sketch the graph of the function f(x) = x + |x|.
1 answer:
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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<h3>Answer:</h3>
- f(1) = 2
- No. The remainder was not 0.
Synthetic division is quick and not difficult to learn. The number in the upper left box is the value of x you're evaluating the function for (1). The remaining numbers across the top are the coefficients of the polynomial in decreasing order by power (the way they are written in standard form). The number at lower left is the same as the number immediately above it—the leading coefficient of the polynomial.
Each number in the middle row is the product of the x-value (the number at upper left) and the number in the bottom row just to its left. The number in the bottom row is the sum of the two numbers above it.
So, the number below -4 is the product of x (1) and 1 (the leading coefficient). That 1 is added to -4 to give -3 on the bottom row. Then that is multiplied by 1 (x, at upper left) and written in the next column of the middle row. This proceeds until you run out of numbers.
The last number, at lower right, is the "remainder", also the value of f(x). Here, it is 2 (not 0) for x=1, so f(1) = 2.