Question

The graph represents the piecewise function

Answer 1

The piece-wise function is defined as follows:

• $f(x) = x^2, 0 \leq x < 3$.

• $f(x) = -\frac{5}{3}x + 14, 3 < x \leq 6$.

• $f(x) = \frac{3}{2}x - 5, 6 \leq x \leq 10$.

What is a piece-wise function?

A piece-wise function is a function that has multiple definitions, depending on the input.

In this graph, for x at least 0 and less than 3, the parabolic curve passes through (0,0), (1,1), (2,4) and has an open interval at (3,9), hence the definition is:

$f(x) = x^2, 0 \leq x < 3$

For x greater than 3 and at most 6, it is a line going through (3,9) and (6,4), hence:

$m = \frac{9 - 4}{3 - 6} = -\frac{5}{3}$

$f(x) = -\frac{5}{3}x + b$

Goes through (3,9), hence:

$9 = -\frac{5}{3}(3) + b$

b = 14.

So

$f(x) = -\frac{5}{3}x + 14, 3 < x \leq 6$

For x between 6 and 10, it is a line going through (6,4) and (10,10), hence:

$m = \frac{10 - 4}{10 - 6} = \frac{6}{4} = \frac{3}{2}$

Then:

$f(x) = \frac{3}{2}x + b$

When x = 10, f(x) = 10, hence:

$10 = \frac{3}{2}(10) + b$

10 = 15 + b

b = -5.

Hence:

$f(x) = \frac{3}{2}x - 5, 6 \leq x \leq 10$

More can be learned about piece-wise functions at brainly.com/question/24734454

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