# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-5/9

Exercises: Try Out - Set 5: Real exam simulation to sharpen your skills and build confidence. - Problem 9

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## Exercise 9

### Question

import { QuestionGraph } from "../graph";

export const metadata = {
  title: "Problem 9",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

Given the following graph:

<QuestionGraph title="Function Graph" description="Inequality System and Graph." />

Given <InlineMath math="4" /> statements:

1. Point <InlineMath math="A (0, -1)" />.
2. Point <InlineMath math="B (1, 0)" />.
3. Point <InlineMath math="C (2, 0)" />.
4. Point <InlineMath math="D (2, 2)" />.

The correct statement is ...


### Choices

- [x] $$1$$, $$2$$, and $$3$$
- [ ] $$1$$ and $$3$$
- [ ] $$2$$ and $$4$$
- [ ] $$4$$ only
- [ ] $$1$$, $$2$$, $$3$$, and $$4$$

### Answer & Explanation

export const metadata = {
  title: "Solution to Problem 9",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

We verify each statement based on the functions provided in the graph:
Exponential function: <InlineMath math="y = 2^x - 2" />
Linear function: <InlineMath math="y = -2x + 4" />

#### Checking Point A

Point <InlineMath math="A" /> is the y-intercept of the exponential curve (<InlineMath math="x=0" />).
<MathContainer>
  <BlockMath math="y = 2^0 - 2 = 1 - 2 = -1" />
</MathContainer>
So, <InlineMath math="A(0, -1)" />. Statement <InlineMath math="(1)" /> is **TRUE**.

#### Checking Point B

Point <InlineMath math="B" /> is the x-intercept of the exponential curve (<InlineMath math="y=0" />).
<MathContainer>
  <BlockMath math="0 = 2^x - 2 \Rightarrow 2^x = 2 \Rightarrow x = 1" />
</MathContainer>
So, <InlineMath math="B(1, 0)" />. Statement <InlineMath math="(2)" /> is **TRUE**.

#### Checking Point C

Point <InlineMath math="C" /> is the x-intercept of the linear line (<InlineMath math="y=0" />).
<MathContainer>
  <BlockMath math="0 = -2x + 4 \Rightarrow 2x = 4 \Rightarrow x = 2" />
</MathContainer>
So, <InlineMath math="C(2, 0)" />. Statement <InlineMath math="(3)" /> is **TRUE**.

#### Checking Point D

Point <InlineMath math="D" /> is the intersection point or a point on the line. The statement claims <InlineMath math="D(2, 2)" />.
If we test coordinate <InlineMath math="(2, 2)" /> into the line equation <InlineMath math="y = -2x + 4" />:
<MathContainer>
  <BlockMath math="y = -2(2) + 4 = -4 + 4 = 0" />
</MathContainer>
The result is <InlineMath math="y = 0" />, not <InlineMath math="2" />. Thus, point <InlineMath math="(2, 2)" /> does not lie on the line <InlineMath math="y = -2x + 4" />.
Statement <InlineMath math="(4)" /> is **FALSE**.

Conclusion: Statements <InlineMath math="(1)" />, <InlineMath math="(2)" />, and <InlineMath math="(3)" /> are correct.


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