Question 3
Answer: Choice A) {(3,4) (3,5)}
-----------
Step-by-step explanation:
Note how in choice A we have repeated x values
x = 3 pairs up with y = 4 and y = 5 at the same time.
The input x = 3 must only pair up with one output only if we want a function to happen.
If you plotted the points (3,4) and (3,5), it is possible to draw a vertical line through them. So this fails the vertical line test.
The other answer choices do not have repeated x values, so they are all functions.
==========================================
Question 4
Answer: choice A) 2x+3y = 10 and choice D) y = 18
-----------
If you plotted choice A and choice D on an xy coordinate system, you should see straight lines forming.
2x+3y = 10 turns into y = (-2/3)x+10/3 which is y = mx+b form.
Choice D's equation is equivalent to y = 0x+18, so its slope here is 0, making it a flat horizontal line.
Choice B does not count as an answer because while it is a linear vertical line, it is not a function for similar reasons back in question 3. The fact that x = 16 pairs up with infinitely many y values is what makes this not be a function.
Choice C is not a linear equation. Instead it is a quadratic equation because the largest exponent is 2.