these questions are for practice, they don't count as points, but i don't understand how to solve them.. can someone please explain them to me??
which function rule represents the data in the table below?
input|1| 2| 3| 4|5
output|9|15|21|27|33
A)y=4+5x
B)y=3+6x
C)y=5+4x
D)y=6+3x
Which function rule represents the data in the table?
x|-3|-2|-1|0|1
y|-1| 2| 5|8|11
A)y=-3x-8
B)y=1/3x-8
C)y=1/3x+8
D)y=3x+8
Which quadratic rule represents the data table?
x|-1|0|1|2|3
y| 6|5|6|9|14
A)y=2x^2+5
B)y=-x^2
C)y=x^2+5
D)y=x^2+5
I don't exactly understand these questions.. @Writeacher or @Mrs. Sue can you help me?
input|1| 2| 3| 4|5
output|9|15|21|27|33
Note that y increases by 6 for each increase of 1 in x. So, your rule will look like
y = 6x
But, using x=1, 6x=6, but y=9. So, we're too low by 3. That means
y = 3+6x
You can easily verify that this rule works for the other entries in the table.
Similarly, for
x|-3|-2|-1|0|1
y|-1| 2| 5|8|11
y grows by 3 for each 1 in x. So, try
y = 3x
But 3(-3) = -9, so that means
y = 3x+8
For the quadratic,
x|-1|0|1|2|3
y| 6|5|6|9|14
Note that f(-1) = f(1). That means the vertex is midway between them, at x=0. Since y(0) = 5, we try
y = (x-0)^2+5 = x^2+5
You can see that that rule works for all the table entries.
Thank you so so much, i understand now :)
which quadratic rule represents the data in the table? x: -1|0|1|2|3| y:-4|-5|-4| -1|4|
I also need help! thanks
which quadratic rule represents the data in the table? x: -1|0|1|2|3|
y:-4|-5|-4| -1|4|
I also need help! thanks
Of course! I'll be happy to help you understand and solve these questions.
Let's start with the first question. The table shows a set of input and output values. To identify the correct function rule, we need to look for a pattern between the input and output values. In this case, if we examine the outputs, we can see that they increase by 6 each time. This means that the output is dependent on multiplying the input by 6 (since 6*1=6, 6*2=12, 6*3=18, and so on).
Now, we need to find the constant term in the function rule. When the input is 0, the output is 9, which means there must be an additional constant term of 9.
Putting it all together, the correct function rule that represents the data in the table is:
B) y = 3 + 6x
Moving on to the second question, here we have another table with input and output values. To find the correct function rule, let's look for a pattern. If we examine the outputs, we can observe that they increase by 3 each time. Therefore, the output is dependent on adding 3 times the input value.
Now, let's find the constant term in the function rule. When the input is 0, the output is -8, so there must be an additional constant term of -8.
Combining everything, the correct function rule that represents the data in the table is:
A) y = -3x - 8
Lastly, for the third question, we are given a table with input and output values. To determine the quadratic rule, let's examine the pattern between the input and output values. If we compare the outputs, we can see that they increase with the square of the input value. This suggests that our quadratic rule should include an x² term.
Now, let's look for the constant term. When the input is 0, the output is 5, so there must be an additional constant term of 5.
Putting all the information together, the correct quadratic rule that represents the data in the table is:
C) y = x² + 5
I hope this explanation helps you understand how to solve these questions! Let me know if you have any further doubts.