Question

the ph of a solution is a measure of how acidic it is. the greater the acidity, the lower the ph. the function \\(f(x) = -\log x\\) gives the ph of a solution, where \\(x\\) is the concentration of hydrogen ions, in moles per liter.

the graph of \\(f(x) = -\log x\\) is a reflection in the x-axis of the graph of \\(g(x) = \log x\\).

graph the ph function using the graphing utility. then answer the questions.
what is the ph of lemon juice that has a hydrogen ion concentration of 0.01 moles per liter?
the ph is 2.

what is the hydrogen ion concentration of orange juice that has a ph of 1?

Explanation:

Identify the transformation of the graph

Using the Function Reflections and Logarithmic Functions knowledge points

$$ f(x) = -\log x = -g(x) $$

Since \(f(x)\) is obtained by multiplying the entire function \(g(x)\) by \(-1\), the graph of \(f(x)\) is a reflection in the \(x\)-axis of the graph of \(g(x) = \log x\).

Calculate the pH of lemon juice

Using the pH Scale Calculations knowledge point

$$
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Calculate the hydrogen ion concentration of orange juice

Using the pH Scale Calculations knowledge point

$$
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The hydrogen ion concentration is \(0.1\) moles per liter.

Answer:

Question 1

The graph of \(f(x) = -\log x\) is a reflection in the x-axis of the graph of \(g(x) = \log x\).

Question 2

The pH is 2.

Question 3

The hydrogen ion concentration of orange juice that has a pH of 1 is 0.1 moles per liter (or \(10^{-1}\) moles per liter).