What is the image of (5, -7) after a reflection over the x-axis?

1 answer:

ki77a [65]3 years ago

5 0

Answer:(5,7)

Step-by-step explanation:

I use this graph/graphing calculator or remember this rule

When theres a reflection over the x axis, all the X values say the same and all of the y values are the opposite.

x=5 y=-7 the x aka 5 stays the same and the opposite of -7 is 7

(5,-7) Turns into (5,7)

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Serga [27]

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3 years ago

myrzilka [38]

Answer:

$\displaystyle f'(x) = \frac{4}{x^2}$

General Formulas and Concepts:

Calculus

Limits

Differentiation

The definition of a derivative is the slope of the tangent line: $\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}$

Step-by-step explanation:

Step 1: Define

Identify.

$\displaystyle f(x) = -\frac{4}{x}$

Step 2: Differentiate

[Function] Substitute in x: $\displaystyle f(x + h) = -\frac{4}{x + h}$
Substitute in functions [Definition of a Derivative]: $\displaystyle f'(x) = \lim_{h \to 0} \frac{-\frac{4}{x + h} - \big( -\frac{4}{x} \big)}{h}$
Simplify: $\displaystyle f'(x) = \lim_{h \to 0} \frac{4}{x(x+ h)}$
Evaluate limit [Limit Rule - Variable Direct Substitution]: $\displaystyle f'(x) = \frac{4}{x(x+ 0)}$
Simplify: $\displaystyle f'(x) = \frac{4}{x^2}$