Question

question
graph the following function on the axes provided.
$f(x)=\

$$\begin{cases}4x + 17&\\text{for}&x < -3\\\\-2&\\text{for}&x > 0\\end{cases}$$

$
click and drag to make a line. click the line to delete it.
click on an endpoint of a line to change it.
answer attempt 1 out of 2
submit answer

Explanation:

Step1: Analyze the first piece \( f(x) = 4x + 17 \) for \( x < -3 \)

This is a linear function. Let's find two points to plot the line. When \( x = -3 \), \( f(-3) = 4(-3) + 17 = -12 + 17 = 5 \). But since the domain is \( x < -3 \), the point \( (-3, 5) \) is an open circle. Let's take another point, say \( x = -4 \), then \( f(-4) = 4(-4) + 17 = -16 + 17 = 1 \). So we have the point \( (-4, 1) \). We can draw a line through these points (with an open circle at \( x = -3 \)) for \( x < -3 \).

Step2: Analyze the second piece \( f(x) = -2 \) for \( x > 0 \)

This is a horizontal line. For any \( x > 0 \), the \( y \)-value is \( -2 \). So we can plot points like \( (1, -2) \), \( (2, -2) \), etc. The point at \( x = 0 \) is an open circle since the domain is \( x > 0 \). We draw a horizontal line at \( y = -2 \) starting from \( x > 0 \) (open circle at \( (0, -2) \)).

Answer:

To graph the function:

• For \( y = 4x + 17 \) ( \( x < -3 \) ): Plot an open circle at \( (-3, 5) \), then draw a line through points like \( (-4, 1) \), \( (-5, -3) \) (calculated as \( 4(-5)+17 = -20 + 17 = -3 \)) etc., for \( x < -3 \).
• For \( y = -2 \) ( \( x > 0 \) ): Plot an open circle at \( (0, -2) \), then draw a horizontal line to the right (e.g., through \( (1, -2) \), \( (2, -2) \), etc.) for \( x > 0 \).

(Note: Since the problem is about graphing, the final answer is the graphical representation as described above. If a numerical answer was required, but in this case, it's a graphing task. The key is to plot the two pieces with open circles at the endpoints of their domains.)