Have you ever been swimming in a pool, and your eyes were red when you get out? this means the chemicals in the pool were not adjusted correctly! more specifically, the measurement of the pool's ph was not quite right.

ph is a measurement of hydronium ions and can be modeled by the function f(x) = −log10x. the variable x represents the amount of hydronium ions, and f(x) gives the ph level.

different liquids have ideal ph values that are different. water at 25 degrees celsius has a ph of 7. anything that has a ph less than 7 is called acidic, and a ph above 7 is basic, or alkaline. seawater has a ph just more than 8, whereas lemonade has a ph of approximately 3.

create a graph of the ph function either by hand or using technology. locate on your graph where the ph value is 0 and where it is 1. you may need to zoom in on your graph.
use your graph to find the ideal ph level if the amount of hydronium ions is raised to 0.50.
the pool company developed new chemicals that transform the ph scale. using the ph function f(x) = −log10x as the parent function, explain which transformation results in a y-intercept and why. you may graph by hand or using technology. be sure to label each transformation on the graph.
f(x) + 1
f(x + 1)

1) (1,0) 2) (0.1, 1) 3) 0.3 4) f(x) +1 does not result in y-intercept f(x+1) intercepts at (0,0)

Step-by-step explanation:

Given the Function for point of Hydrogen (pH):

1) When pH=0 we have (1,0) for this function since we plug 0 for y and get x.

2) When the pH is 1, the y-coordinate is 1 when plugged the Domain (x) is 1/10.

3) The x, in this function indicates the level of Hidronium while the y the pH. So plugging in:

4)

This function does not result in a y-intercept. A y-intercept needs a coordinate point in (x,y), since x -log0 is not defined, does not exist the curve passes right close but never touches the y-axis intercepting it.

This function has only one interception. At the origin. (0,0)

Here's what I find.

Step-by-step explanation:

pH = f(x) = -log₁₀x

1. Graphs

I used Excel to calculate the pH values and draw the graphs (see the Figure).

f(x) and f(x) +1 are plotted against the left-hand axis, while f(x+ 1) is plotted against the expanded right-hand axis.

The points at which pH = 0 and pH = 1 are indicated by the large red dots.

2. x = 0.5

When x = 0.5, pH ≈0.30. The point is indicated by the red diamond.

3. Transformations

(a) ƒ(x) = -log(x) + 1

This function has no y-intercept, because log(0) is undefined.

(b) ƒ(x +1) = -log(x + 1)

f(0) = -log(0 + 1) = -log(1) = 0

This function has a y-intercept at (0,0).

step-by-step explanation:

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