Question

75 POINTS PLEASE RESPOND ASAP

Answer 1

ANSWER :

The pH level of a swimming pool indicates the level of acidity or alkalinity

of the swimming pool.

Correct Responses;

First Part:  Please find attached the required graph of the pH function created with MS Excel.

The pH value is 0 when x = 1

The pH value is 1 when x = 0.1

The pH level if the hydronium ions is raised to 0.50 is approximately 0.301029996.

Second Part: The transformation that results in a y-intercept is f(x + 1), because f(0 + 1) exists and is equal to 0.

STEPS

Method by which the above responses are obtained

First part

The given pH function is f(x) = -㏒₁₀x

Where;

x = The amount of hydronium ions

A substance with a pH < 7 is acidic

A substance with a pH > 7 is alkaline

A neutral solution has pH = 7

Water is a neutral solution

The graph of the pH function created with MS Excel is attached

The table of values of the graph is as follows;

From the graph, we have;

When the pH value is 0, the hydronium ion concentration is 1

The pH value is 1 when x = 1 × 10⁻¹ = 0.1

The pH level if the hydronium ions, x = 0.5 is given from the graph as follows;

pH = f(0.5) = -㏒₁₀(0.5) ≈ 0.301029996

The pH value when the hydronium ions is 0.5 is pH ≈ 0.301029996

Second Part

Using f(x) = -㏒₁₀x as the parent function, the graph of f(x) + 1, and f(x + 1) are plotted

From the graph, we have;

The graph of f(x) + 1 = -㏒₁₀x + 1

The graph of f(x + 1) = The graph of -㏒₁₀(x + 1)

At the y-intercept, x = 0, therefore;

f(x) + 1 = f(0) + 1 = -㏒₁₀0 + 1 = Undefined

f(x + 1) = f(0 + 1) = -㏒₁₀(0 + 1) = 0

Therefore;

The transformation that results in a y-intercept is f(x + 1) because f(0 + 1) is 0, which is defined.

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