Question

Consider the following function.

h(x)=−4x−8 if x≤−2

1/2x2 ifx>−2

Identify the general shape and direction of the graph of this function on the interval (−∞,−2].

Answer 1

@tranquility

Answer 2

@vocaloid

Answer 3

The interval (−∞,−2] means that the x-value can be anything from -2 all the way to -100 to -1000 to -100000 to negative infinity

The question says that the function will have a graph of h(x)= −4x−8 if x≤−2

Whenever x is less than or equal to -2, it will look like the equation y = -4x-8

The answer choices want you to select a graph that has the general shape and direction of it.

For the equation y = -4x -8

Is it a linear equation? Is a quadratic equation? Is it a cubic equation?
Does it have a positive slope or a negative slope?

Answer 4

it is linear

Answer 5

Which of your answer choices shows a linear line?

Is the slope of the line going to be positive or negative?

What's your final answer then?

Answer 6

slope : -4

Answer 7

the fourth one

Answer 8

Would that be the bottom left image?

Answer 9

yes

Answer 10

That is correct

Answer 11

i have another one

Answer 12

What do you think the answer is?

The interval is from -2 to infinity.
This corresponds to the equation 1/2 x^2 because it's domain is x>-2

What is the general graph for 1/2 x^2 going to look like?

Answer 13

The general graph for 1/2 x^2 is going to be the graph of y = x^2

Answer 14

the fourth one on the bottom to the left

Answer 15

You've posted the same image 3 times

Answer 16

no it's different pictures of the question

Answer 17

oh no wait you're right

Answer 18

Yes, it is going to be the left most one on the bottom row

Answer 19

For the final question, remember the answers for the previous two parts?

Along the x-axis from the left side until you approach negative 2, you will have a linear line with a negative slope.

And then from -2 to infinity, you will have a quadratic function

Answer 20

From negative infinity to -2 it's the linear line. And since it's x≤−2 that means we INCLUDE -2 in the linear line.

The way you depict that in the graph is by shading the circle.

The other graph is x>-2 so the -2 is NOT included so it has an empty circle.

Answer 21

okay, that'd be 2nd picture on the first picture

Answer 22

That is correct!

Answer 23

really

Answer 24

Yes! :)

Answer 25

@tranquility

Answer 26

@tranquility