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).
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Answer:
The pool is being filled
Step-by-step explanation:
The function definition tells you ...
f(5) = the volume of water in the pool 5 minutes after they start
f(10) = the volume of water in the pool 10 minutes after they start
So, the inequality ...
f(5) < f(10)
means the volume of water in the pool 10 minutes after they start is greater than it is 5 minutes after they start. In short, <em>they are filling the pool</em>.
The expression can represent the value of x in terms of R, m, n and k after rearranging.
<h3>What is an expression?</h3>
It is defined as the combination of constants and variables with mathematical operators.
It is given that:
The expression is:
Square both side:
16m² x n = R²k³
x = (R²k³)/(16m²n)
The above expression represents the value of x in terms of R, m, n and k.
Thus, the expression can represent the value of x in terms of R, m, n and k after rearranging.
Learn more about the expression here:
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