# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-6/19

Exercises: Try Out - Set 6: Real exam simulation to sharpen your skills and build confidence. - Problem 19

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## Exercise 19

### Question

export const metadata = {
  title: "Problem 19",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

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

Given the following graph:

<Graph title="Function Graph" description="Graph of linear and exponential functions." />

1. point <InlineMath math="A(0, -2)" />
2. point <InlineMath math="B(0, 6)" />
3. point <InlineMath math="C(-3, 0)" />
4. point <InlineMath math="D(-2, 2)" />

The correct statements are


### 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 for Problem 19",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

We will check the validity of each statement based on the given graph. The graph consists of the line <InlineMath math="y = 2x + 6" /> and the exponential curve <InlineMath math="y = (1/2)^x - 3" />.

#### Analysis of Statement 1

Point A is the y-intercept of the curve <InlineMath math="y = (1/2)^x - 3" />. Substitute <InlineMath math="x = 0" />:

<BlockMath math="y = \left(\frac{1}{2}\right)^0 - 3 = 1 - 3 = -2" />

So, point A is <InlineMath math="(0, -2)" />. Statement <InlineMath math="1" /> is **correct**.

#### Analysis of Statement 2

Point B is the y-intercept of the line <InlineMath math="y = 2x + 6" />. Substitute <InlineMath math="x = 0" />:

<BlockMath math="y = 2(0) + 6 = 6" />

So, point B is <InlineMath math="(0, 6)" />. Statement <InlineMath math="2" /> is **correct**.

#### Analysis of Statement 3

Point C is the x-intercept of the line <InlineMath math="y = 2x + 6" />. Substitute <InlineMath math="y = 0" />:

<BlockMath math="\begin{aligned} 2x + 6 &= 0 \\ 2x &= -6 \\ x &= -3 \end{aligned}" />

So, point C is <InlineMath math="(-3, 0)" />. Statement <InlineMath math="3" /> is **correct**.

#### Analysis of Statement 4

Statement <InlineMath math="4" /> states that point D is <InlineMath math="(-2, 2)" />. On the graph, D is the intersection point of the line and the curve. We check if the point <InlineMath math="(-2, 2)" /> lies on both functions.

For the line <InlineMath math="y = 2x + 6" />:

<BlockMath math="y = 2(-2) + 6 = -4 + 6 = 2" />

Point <InlineMath math="(-2, 2)" /> is on the line.

For the curve <InlineMath math="y = (1/2)^x - 3" />:

<BlockMath math="y = \left(\frac{1}{2}\right)^{-2} - 3 = 2^2 - 3 = 4 - 3 = 1" />

Since <InlineMath math="y = 1 \neq 2" />, point <InlineMath math="(-2, 2)" /> is not on the curve. Therefore, D is not <InlineMath math="(-2, 2)" />. Statement <InlineMath math="4" /> is **incorrect**.

Thus, the correct statements are <InlineMath math="1" />, <InlineMath math="2" />, and <InlineMath math="3" />.


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