Question

1. which graph represents a linear function?

a. graph a
b. graph b
c. graph c
d. graph d

1. which equation represents a nonlinear function?

a. $y = x$
b. $y = 2x$
c. $y = x^2$
d. $y = x + 2$

Explanation:

Question 29

A linear function has a graph that is a straight line (constant slope) and can be represented as \( y = mx + b \) (linear equation).

• Option a: Curved graph (non - linear, like exponential or logarithmic).
• Option b: Discrete points (not a continuous linear graph).
• Option c: Straight line (matches linear function's graph).
• Option d: Wavy curve (non - linear, multiple peaks/troughs).

A linear function has the form \( y=mx + b \) (degree 1 in \( x \)), while a non - linear function has a degree other than 1.

• Option a: \( y = x \) is \( y=1x + 0 \) (linear, degree 1).
• Option b: \( y = 2x \) is \( y = 2x+0 \) (linear, degree 1).
• Option c: \( y=x^{2} \) has degree 2 (quadratic, non - linear).
• Option d: \( y=x + 2 \) is \( y = 1x+2 \) (linear, degree 1).

Answer:

C. The graph with a straight line (the one in option c)

Question 30