F(x)=∣x∣
1 answer:
Answer:
Step-by-step explanation:
There are two transformations, one vertical, one horizontal.
The + 9 part outside the absolute value sign moves the graph up 9 units.
Replacing x with x - 1 moves the graph right 1 unit.
<em>Comment:</em> The horizontal shifts sometimes appear backwards: x - 1 looks like a shift to the left, but it's not.
Example: f(4) = |4| = 4. To get the same output (4) from g(x), you have to use a value for x that is 1 unit <u>larger</u> than 4. g(5) = |5 - 1| = 4.
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Hello!
6.
Since the area is that of a square, you know that all side lengths are the same.
Area is base times height (A = bh), but since base and height are the same for a square, you get the formula A = a².
The length of the side of a square with an area of 144 in² is 12 in.
7.
Rational number.
8.
This is a right triangle; use the Pythagorean Theorem to find missing lengths of right triangles. Pythagorean Theorem: a² + b² = c², where c is the hypotenuse of the triangle.
Plug in your leg lengths:
a² + b² = c²
8² + x² = 21²
64 + x² = 441
x² = 377
x = 19.4
6.
Since the area is that of a square, you know that all side lengths are the same.
Area is base times height (A = bh), but since base and height are the same for a square, you get the formula A = a².
The length of the side of a square with an area of 144 in² is 12 in.
7.
Rational number.
8.
This is a right triangle; use the Pythagorean Theorem to find missing lengths of right triangles. Pythagorean Theorem: a² + b² = c², where c is the hypotenuse of the triangle.
Plug in your leg lengths:
a² + b² = c²
8² + x² = 21²
64 + x² = 441
x² = 377
x = 19.4