The graph of the pH function can be created by plotting the output of
input values of the hydronium ions, <em>x</em>, in the range 0 < x ≤ 1.
Correct responses:
First part:
Please find attached the graph of the pH function
From the attached graph of the pH function, we have;
- The point where the pH value is 0 is
- The point where the pH value is 1 is
- The pH level if the hydronium ion is raised to 0.50 is approximately <u>0.3</u>
Second part
- Please find attached the graph of the transformations, f(x) + 1, and f(x + 1) of the parent log function.
- The transformation that results in a y-intercept is
, because, at x = 0, f(x + 1) = 0.
First part
The pH function is; f(x) = -log₁₀x
Please find attached the graph of the pH function created with MS Excel
Where;
x = Amount of hydronium ions
f(x) = pH level
When the pH is 0, we have;
-log₁₀x = 0
Which gives;
x = 10⁰ = 1
- When the pH value is 0, the point on the graph is
When the pH value is 1, we have;
-log₁₀x = 1
log₁₀x = -1
x = 10⁻¹ = 0.1
- The point on the graph where the pH value is 1 is
- From the graph, the ideal pH level if the amount of hydronium ions is raised to 0.50 is pH = 0.301029996 ≈ <u>0.30</u>
Second Part
The given transformations are;
f(x) + 1, and f(x + 1)
- <u>The graph of the transformations created with MS Excel is attached</u>
At the y-intercept, x = 0
From the transformation, f(x) + 1, we have;
At x = 0, the transformation = -log₁₀(0) + 1
log₁₀(0) = Does not exist (DNE)
Therefore;
f(x) + 1 = -log₁₀(0) + 1 = DNE
The transformation, f(x + 1), at x = 0, gives;
f(0 + 1) = -log₁₀(0 + 1) = -log₁₀(1) = 0
Therefore;
The function f(x + 1) = -log₁₀(x + 1) is defined at x = 0, and therefore, has a y-intercept
- The transformation that has a y-intercept is
Learn more about the pH values here:
