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balandron [24]
2 years ago
5

Which graph is the result of reflecting f(x) = One-fourth(8)x across the y-axis and then across the x-axis? On a coordinate plan

e, an exponential function approaches y = 0 in quadrant 2 and incresaes into quadrant 1. It goes through the y-axis at (0, 0.25) and goes through (1, 2). On a coordinate plane, an exponential function approaches y = 0 in quadrant 1 and increases in quadrant 2. It crosses the y-axis at (0, 0.25) and goes through (negative 1, 2). On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It crosses the y-axis at (0, negative 0.25) and goes through (1, negative 2). On a coordinate plane, an exponential funtion increases in quadrant 3 into quadrant 4 and approaches y = 0. It goes through (negative 1, negative 2) and crosses the y-axis at (0, negative 0.25).
Mathematics
2 answers:
VladimirAG [237]2 years ago
8 0

Answer:

Its B

Explanation:

I just answered it.

scoundrel [369]2 years ago
7 0

Answer:

Which graph is the result of reflecting f(x) = One-fourth(8)x across the y-axis and then across the x-axis?

On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and incresaes into quadrant 1. It goes through the y-axis at (0, 0.25) and goes through (1, 2).

On a coordinate plane, an exponential function approaches y = 0 in quadrant 1 and increases in quadrant 2. It crosses the y-axis at (0, 0.25) and goes through (negative 1, 2).

On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It crosses the y-axis at (0, negative 0.25) and goes through (1, negative 2).

On a coordinate plane, an exponential funtion increases in quadrant 3 into quadrant 4 and approaches y = 0. It goes through (negative 1, negative 2) and crosses the y-axis at (0, negative 0.25).

Step-by-step explanation:

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Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 – 10x +2?
zhuklara [117]

Answer:

  • <em>The translation that maps the vertex of the graph of the function f(x) = x² onto the vertex of the function g(x) = x² - 10x + 2 is </em><u>5 units to the right and 23 units down.</u>

Explanation:

<u>1) </u><u>Vertex form</u><u> of the function that represents a parabola.</u>

The general form of a quadratic equation is Ax² + Bx + C = 0, where A ≠ 0, and B and C may be any real number. And the graph of such equation is a parabola with a minimum or maximum value at its vertex.

The vertex form of the graph of such function is: A(x - h)² + k

Where, A a a stretching factor (in the case |A| > 1) or compression  factor (in the case |A| < 1) factor.

<u>2) Find the vertex of the first function, f(x) = x²</u>

This is the parent function, for which, by simple inspection, you can tell h = 0 and k = 0, i.e. the vertex of f(x) = x² is (0,0).

<u>3) Find teh vertex of the second function, g(x) = x² -10x + 2</u>

The method is transforming the form of the function by completing squares:

  • Subtract 2 from both sides: g(x) - 2 = x² - 10x

  • Add the square of half of the coefficient of x (5² = 25) to both sides: g(x) - 2 + 25 = x² - 10x + 25

  • Simplify the left side and factor the right side: g(x) + 23 = (x - 5)²

  • Subtract 23 from both sides: g(x) = (x - 5)² - 23

That is the searched vertex form: g(x) = (x - 5)² - 23.

From that, using the rules of translation you can conclude immediately that the function f(x) was translated 5 units horizontally to the right and 23 units vertically downward.

Also, by comparison with the verex form A(x - h)² + k, you can conclude that the vertex of g(x) is (5, -23), and that means that the vertex (0,0)  was translated 5 units to the right and 23 units downward.

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