Both f(x) and g(x) have the same range of [0,-infinity).
<h3>What is a function?</h3>A function is an expression that shows the relationship between two or more numbers and variables.
Plotting the functions f(x) = 2x² – 3x + 5 and g(x) = 2ˣ - 5:
Both f(x) and g(x) have the same range of [0,-infinity).
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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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