Question If a function is defined by Evaluate f(-3), f(-1), and f(0) a | Basic Mathematics 2079

Basic Mathematics207910 marksNumerical: piecewise function, continuityDiscontinuity types

Question

If a function is defined by $f(x) = \begin{cases} 1 + x & \text{if } x \leq -1 \\ x^2 & \text{if } x > -1 \end{cases}$

Evaluate $f(-3)$ , $f(-1)$ , and $f(0)$ and sketch the graph. Define different types of discontinuity at a point. At what points the function becomes continuous of the function $f(x) = \frac{x-2}{x^2-7x+10}$ [5+5]

Question

If a function is defined by $$f(x) = \begin{cases} 1 + x & \text{if } x \leq -1 \ x^2 & \text{if } x > -1 \end{cases}$$

Evaluate $f(-3)$, $f(-1)$, and $f(0)$ and sketch the graph. Define different types of discontinuity at a point. At what points the function becomes continuous of the function $$f(x) = \frac{x-2}{x^2-7x+10}$$ [5+5]

Given data: $f(x) = \begin{cases} 1 + x & \text{if } x \leq -1 \\ x^2 & \text{if } x -1 \end{cases}$ Points to evaluate: $x = -3,\ -1,\ 0$ . Since $-3 \leq -1$ , use the first piece $f(x) = 1 + x$ : $f(-3) = 1 + (-3) = \boxed{-2}$ Since $-1 \leq -1$ , use the first piece $f(x) = 1 + x$ : $$f(-1) =...

Given data: $$f(x) = \begin{cases} 1 + x & \text{if } x \leq -1 \ x^2 & \text{if } x -1 \end{cases}$$ Points to evaluate: $x = -3,\ -1,\ 0$. Since $-3 \leq -1$, use the first piece $f(x) = 1 + x$: $$f(-3) = 1 + (-3) = \boxed{-2}$$ Since $-1 \leq -1$, use the first piece $f(x) = 1 + x$: $$f(-1) =...

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Question If a function is defined by Evaluate f(-3), f(-1), and f(0) and sketch the graph. Define different types of discontinuity at a point. At what points the function becomes continuous of the function [5+5]