Question

Question
Graph the function f(x)=32x−4
.

Answer 1

the graph ranges from 10- -10

Answer 2

To graph the function \( f(x) = 32x - 4 \), follow these steps:

1. **Identify the function type**: \( f(x) = 32x - 4 \) is a linear function, which means its graph will be a straight line.

2. **Calculate the y-intercept**: The y-intercept occurs when \( x = 0 \).
\[
f(0) = 32(0) - 4 = -4
\]
So, the y-intercept is \( (0, -4) \).

3. **Calculate the slope**: The slope \( m \) of the linear function can be identified from the equation \( y = mx + b \), where \( m = 32 \) and \( b = -4 \). This means for each unit increase in \( x \), \( f(x) \) increases by \( 32 \).

4. **Plot the y-intercept**: Start by plotting the point \( (0, -4) \) on the Cartesian plane.

5. **Use the slope to find another point**: From the y-intercept, you can count up 32 units and 1 unit to the right to find another point. Starting from \( (0, -4) \):
- Move 1 unit right to \( x = 1 \)
- Move up \( 32 \) units: \( -4 + 32 = 28 \)
- This gives you the point \( (1, 28) \).

6. **Draw the line**: Use a ruler to draw a straight line through the points \( (0, -4) \) and \( (1, 28) \). Extend the line in both directions.

7. **Label the axes**: Make sure to label the x-axis and y-axis appropriately.

Now, you can visualize the graph with a straight line crossing the y-axis at -4 and having a steep positive slope of 32. This indicates that the line rises sharply as \( x \) increases.

Answer 3

If you would like to restrict the graph of the function \( f(x) = 32x - 4 \) to the range of \( y \) values between -10 and 10, we need to determine the corresponding \( x \) values for those \( y \) limits.

1. **Set the function equal to -10 to find the corresponding \( x \) value:**
\[
32x - 4 = -10
\]
\[
32x = -10 + 4
\]
\[
32x = -6
\]
\[
x = -\frac{6}{32} = -\frac{3}{16}
\]

2. **Set the function equal to 10 to find the corresponding \( x \) value:**
\[
32x - 4 = 10
\]
\[
32x = 10 + 4
\]
\[
32x = 14
\]
\[
x = \frac{14}{32} = \frac{7}{16}
\]

### Summary of Points
- For \( y = -10 \), \( x \approx -0.1875 \) (or \( -\frac{3}{16} \))
- For \( y = 10 \), \( x = 0.4375 \) (or \( \frac{7}{16} \))

### Graphing Procedure
1. **Plot the line**: First, you will still include the points previously discussed (the y-intercept at (0, -4) and the other point at (1, 28)). However, you will only draw the segment of the line that falls within the specified \( y \) limits.

2. **Plot the points for the y boundaries**:
- Plot \( (-\frac{3}{16}, -10) \) and \( (\frac{7}{16}, 10) \).
- Calculate the y-values at those \( x \) values to observe the segments of the line that are visible.

3. **Draw the segment**: Connect the points \( (-\frac{3}{16}, -10) \) and \( (0, -4) \) and then from \( (0, -4) \) to \( (0.4375, 10) \).

By limiting the graph to \( y \) values between -10 and 10, you'll essentially be visualizing a linear segment of the larger function, rather than the entire infinite line.

If you need further help creating the graph visually or in a specific format, please let me know!