we need to get your brain thinking in this way. that you begin to understand how to do these things.
airways to say that your brain is not working that way, is not a valid excuse. we need to change that. your brain needs to get used to this way of thinking.
so, please, please, PLEASE go through the explanations below and tell me, where exactly in these explanations you stopped understanding what I was saying. so that I can better explain to you what is happening.
1. (0, -2)
2. 4
3. a geometric sequence. the common ratio is -2.0
4. the third option
5. the fourth option
Step-by-step explanation:
1. as x increases, y decreases. until, suddenly after x=0, this tendency reverses, and with increasing x also y increases. so, this is a turning point.
2. look at the line. it only starts with x>0 (it looks like x is around 1).
"input" is all the values of x the function has a defined result for (y = result values).
so, as there is no line for negative x, we can eliminate the first 2 answers.
x=0 is no valid answer either (as mentioned above, the line only starts well after x=0).
in the answer options the only x value having an y value above or below this x value is x=4.
3. look at the difference between 2 numbers next to each other in the sequence.
2.4 to -4.8
-4.8 to 9.6
and so on.
what do we need to do to get from the left to the right ?
we need to multiply by -2.
so, the relationship between "sequence item n" (an) to "sequence item n-1" (an-1) is a ratio, a multiplication factor :
an/an-1 = -2
4. it is completely simple. a function can be many things. on an x/y coordinate grid it can have gaps, it can have sharp direction changes,...
but there us one thing a function can never have : multiple different y values for one x value.
in the first graph x=2 has two different y values (-1 and -3). so, it is not clear what the result for x=2 would be. and that means, it is not a function.
in the second graph x=4 has two different y values.
in the third graph all is OK.
in the fourth graph x=-2 has two different y values.
so, only the third option is a function.
5. this function calculates the height of the thrown rock after t seconds of flight.
therefore, only the fourth answer makes sense.
