## Solve Lesson 47 Page 62 SBT Math 10 – Kite>

Topic

Given the function $$h\left( x \right) = \left\{ \begin{array}{l}1\quad \quad x < 0\\2\quad \quad x \ge 0\end{array} \right.$$

a) Which of the following points is on the graph of the function above: $$A\left( {0;0} \right),B\left( { – 1;1} \right),C\left( { 2021;1} \right);D\left( {2022;2} \right)$$

b) Indicate two points on the graph of the above function with coordinates equal to 2

c) Indicate the point on the graph of the above function whose coordinate is -2022

Solution method – See details

Let$$f\left( x \right) = a{x^2} + bx + c$$

At $$x = {x_0}$$ then $$f\left( {{x_0}} \right) = a{x_0}^2 + b{x_0} + c$$

Detailed explanation

a) + At $$x = 0 \Rightarrow y = h(x) = 2 \Rightarrow A\left( {0;0} \right) \notin h\left( x \right)$$

+ At $$x = – 1 < 0 \Rightarrow y = h(x) = 1 \Rightarrow B\left( { – 1;1} \right) \in h\left( x \right)$$

+ At $$x = 2021 > 0 \Rightarrow y = h(x) = 2 \Rightarrow C\left( {2021;1} \right) \notin h\left( x \right)$$

+ At $$x = 2022 > 0 \Rightarrow y = h(x) = 2 \Rightarrow D\left( {2022;2} \right) \in h\left( x \right)$$

b) We have $$h(x) = 2$$ if $$x \ge 0$$

Therefore, all points with non-negative coordinates have a coordinate of 2.

The set of points with coordinate 2 is $$S = \left\{ {(a;2)|a \ge 0} \right\}$$

For example: $$E\left( {3;2} \right),G\left( {100;2} \right)$$

c) For $$x = – 2022 < 0$$ then $$y = h(x) = 1 \Rightarrow H\left( { – 2022;1} \right)$$