The image shows a set of questions under the title "Uji Pemahaman" related to transformations of functions. The questions focus on reflections of functions across axes and transformations involving linear and quadratic functions. Let's go through the solutions to some of these problems:

1. Reflections of Linear Function over $x = 3$

The original function is $f(x) = \frac{3}{2}x + 12$. We are asked to find the reflection over $x = 3$.

The formula for reflection over $x = c$ is: $g(x) = f(2c - x)$ For $x = 3$, we get: $g(x) = f(6 - x) = \frac{3}{2}(6 - x) + 12 = \frac{3}{2} \cdot 6 - \frac{3}{2}x + 12 = 9 - \frac{3}{2}x + 12 = 21 - \frac{3}{2}x$ So the answer is $g(x) = 21 - \frac{3}{2}x$, which matches option C.

2. Reflections of Linear Function over the Y-axis

The original function is $f(x) = \frac{3}{4}x + 8$. The reflection over the y-axis changes $x$ to $-x$. Therefore: $g(x) = f(-x) = \frac{3}{4}(-x) + 8 = -\frac{3}{4}x + 8$ The answer is $g(x) = -\frac{3}{4}x + 8$, which is option B.

5. Reflection Based on Graph

The graph shows $f(x)$ as the reflection of $g(x)$ across the x-axis. From the image:

• $g(x)$ intersects the y-axis at $2$.
• The reflection across the x-axis will make the y-value at $x = 6$ the opposite of the corresponding $g(x)$ value.

Since $g(x)$ is not shown at $x = 6$, but given the symmetry and reflection, we infer $f(6)$ should equal $-g(6)$. This can be determined if more information is provided, but visually, it looks like $g(6) = 8$, so $f(6) = -8$.

Would you like more detailed steps on a specific question, or clarification on the methods used?

Related Questions:

1. What is the formula for reflecting a function over a vertical line $x = a$?
2. How do reflections over the y-axis affect linear functions?
3. What transformations occur when reflecting a function twice over different axes?
4. How can you deduce properties of a function by looking at its graph after a reflection?
5. What happens to the slope of a line when reflected over the y-axis?

Tip:

When reflecting functions, always consider whether you're reflecting over the x-axis, y-axis, or another vertical line. This changes the reflection rule applied to the function.