The problem provides a linear function $F(x) = 3x - 2$ and asks for the following:

a. Tentukan pasangan atau peta $x = -3, -2, -1, 0, 1, 2$

We need to determine the output of $F(x)$ for each of these $x$-values.

$F(-3) = 3(-3) - 2 = -9 - 2 = -11$ $F(-2) = 3(-2) - 2 = -6 - 2 = -8$ $F(-1) = 3(-1) - 2 = -3 - 2 = -5$ $F(0) = 3(0) - 2 = 0 - 2 = -2$ $F(1) = 3(1) - 2 = 3 - 2 = 1$ $F(2) = 3(2) - 2 = 6 - 2 = 4$

So, the pairs are: $(-3, -11), (-2, -8), (-1, -5), (0, -2), (1, 1), (2, 4)$

b. Tentukan pula pasangan $x = \frac{1}{2}, \frac{3}{4}, \frac{3}{2}$

We need to find $F(x)$ for the fractional values of $x$.

$F\left(\frac{1}{2}\right) = 3\left(\frac{1}{2}\right) - 2 = \frac{3}{2} - 2 = \frac{3}{2} - \frac{4}{2} = -\frac{1}{2}$ $F\left(\frac{3}{4}\right) = 3\left(\frac{3}{4}\right) - 2 = \frac{9}{4} - 2 = \frac{9}{4} - \frac{8}{4} = \frac{1}{4}$ $F\left(\frac{3}{2}\right) = 3\left(\frac{3}{2}\right) - 2 = \frac{9}{2} - 2 = \frac{9}{2} - \frac{4}{2} = \frac{5}{2}$

So, the pairs are: $\left(\frac{1}{2}, -\frac{1}{2}\right), \left(\frac{3}{4}, \frac{1}{4}\right), \left(\frac{3}{2}, \frac{5}{2}\right)$

c. Gambar grafik fungsi $F$ pada kertas grafik

To graph the function $F(x) = 3x - 2$, plot the points calculated in parts (a) and (b), then draw the straight line through these points. Since this is a linear function, the graph will be a straight line with a slope of 3 and a y-intercept of -2.

Would you like a more detailed graph explanation or help with plotting the points?

Relative Questions:

1. What is the slope of the function $F(x) = 3x - 2$?
2. How do you interpret the y-intercept in a linear function?
3. How would the graph change if the function was $F(x) = 3x + 2$?
4. Can you find $F(x)$ for $x = -\frac{1}{2}$?
5. What are the key differences between a linear and a quadratic function graph?

Tip:

When plotting linear functions, start with the y-intercept and use the slope to find other points easily.