Question

y = 3x + 1
(1, 4)
(0, 1)
-4 -3 -2 -1 0 1 2 3 4
○ quadratic○ neither○ linear
type lowercase o twice for ∞. if no interval exists type dne for does not exist.
increasing:
decreasing:
constant:
domain:
range:
question help: message instructor

Explanation:

Step1: Identify function type

The equation $y=3x+1$ follows the linear form $y=mx+b$, where $m=3$ (slope) and $b=1$ (y-intercept).

Step2: Find increasing interval

Slope $m=3>0$, so the function rises for all $x$.
Increasing interval: $(-\infty, \infty)$

Step3: Find decreasing interval

No $x$ values make the function fall.
Decreasing interval: DNE

Step4: Find constant interval

No $x$ values make the function flat.
Constant interval: DNE

Step5: Find domain

Linear functions accept all real $x$.
Domain: $(-\infty, \infty)$

Step6: Find range

Linear functions produce all real $y$.
Range: $(-\infty, \infty)$

Answer:

• Function type: Linear
• Increasing: $(-\infty, \infty)$
• Decreasing: DNE
• Constant: DNE
• Domain: $(-\infty, \infty)$
• Range: $(-\infty, \infty)$