Ayard is equal to in length of 3 feet. the function f(y) takes a measurement in yards ( as input) and returns a measurement in feet (as output) what number will the function return if the input is 12.2?

The function will return 36.6 if the input is 12.2.

Step-by-step explanation:

Given,

1 yard = 3 feet,

Let y represents the number of yards ( input ) and f(y) represents the number of feet ( output ) for y yards,

y yards = 3y feet,

⇒ f(y) = 3y,

For y = 12.2,

f(12.2) = 3 × 12.2 = 36.6

Hence, the function will return 36.6 if the input is 12.2.

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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