Evaluate each function over the domain {-1,0,1,2}. As the values of the domain increase, do the values of the function increase of decrease?
1. y = 3^x
2.y = 3(1/5)^x
^These are the listed equations.
I really need help with this question, cause I am really lost. Could someone help me solve these and write a step by step explanation on how? Thank you!
-Kira
just plug in the domain values.
3^-1 = 1/3
3^0 = 1
and so on
For the function y=b^x, then as x increases
if b > 1, y increases, just as with compound interest
If b < 1, y decreases, as with radioactive decay
The graphs in your text should show this quite clearly.
Well, Kira, let's clown around and evaluate these functions over the given domain {-1, 0, 1, 2}.
1. y = 3^x
First, let's evaluate the function for each value in the domain:
For x = -1: y = 3^(-1) = 1/3
For x = 0: y = 3^0 = 1
For x = 1: y = 3^1 = 3
For x = 2: y = 3^2 = 9
Now, let's see if the values of the function increase or decrease as the values of the domain increase. As we move from -1 to 0 to 1 to 2 in the domain, the values of the function actually increase. It's like the function is going on a hot air balloon ride, getting higher and higher as we move along the domain. Up, up, and away!
2. y = 3(1/5)^x
Let's evaluate the function for each value in the domain:
For x = -1: y = 3(1/5)^(-1) = 15
For x = 0: y = 3(1/5)^0 = 3
For x = 1: y = 3(1/5)^1 = 3/5
For x = 2: y = 3(1/5)^2 = 3/25
Now, let's analyze if the values of the function increase or decrease as the values of the domain increase. As we go from -1 to 0 to 1 to 2 in the domain, the values of the function actually decrease. It's like the function is sliding down a slippery slope, going lower and lower. Watch your step and bring some grip socks!
Remember, this evaluation really depends on the given domain. If the domain was different, the result might be different too. Keep clowning around with math, Kira!
Sure, I can help you with that! Let's evaluate the given functions over the domain {-1, 0, 1, 2}.
1. Function: y = 3^x
To evaluate this function over the given domain, substitute the values of x into the equation and calculate the corresponding values of y.
When x = -1:
y = 3^(-1) = 1/3
When x = 0:
y = 3^0 = 1
When x = 1:
y = 3^1 = 3
When x = 2:
y = 3^2 = 9
Now let's determine if the values of the function increase or decrease as the values of the domain increase.
-1 < 0 < 1 < 2
1/3 < 1 < 3 < 9
As we can see, as the values of the domain increase, the values of the function (y) also increase.
2. Function: y = 3(1/5)^x
Similarly, let's evaluate this function over the given domain.
When x = -1:
y = 3(1/5)^(-1) = 3/5
When x = 0:
y = 3(1/5)^0 = 3
When x = 1:
y = 3(1/5)^1 = 3/5
When x = 2:
y = 3(1/5)^2 = 3/25
Now let's compare the values of the function as the values of the domain increase.
-1 < 0 < 1 < 2
3/5 = 0.6 > 3/5 > 3/25
As we can see, the values of the function in this case fluctuate but do not strictly increase or decrease as the values of the domain increase.
I hope this step-by-step explanation helps you understand how to evaluate the given functions and determine if the values increase or decrease with increasing domain values. Let me know if you have any further questions!
I can definitely help you with that! Let's go through each function step by step.
1. y = 3^x
To evaluate this function over the given domain {-1, 0, 1, 2}, we substitute each value of the domain into the function and calculate the corresponding value of y.
For x = -1:
y = 3^(-1) = 1/3
For x = 0:
y = 3^0 = 1
For x = 1:
y = 3^1 = 3
For x = 2:
y = 3^2 = 9
Now, let's analyze if the values of the function increase or decrease as we go from -1 to 2 in the domain.
-1 < 0 < 1 < 2
We can see that as we increase the values of x from -1 to 2, the corresponding values of y = 1/3, 1, 3, 9 also increase. So in this case, the values of the function y = 3^x increase as the values of the domain increase.
2. y = 3(1/5)^x
Similarly, we will substitute each value of the domain into the function and calculate the corresponding value of y.
For x = -1:
y = 3(1/5)^(-1) = 3(5) = 15
For x = 0:
y = 3(1/5)^0 = 3
For x = 1:
y = 3(1/5)^1 = 3/5 = 0.6
For x = 2:
y = 3(1/5)^2 = 3/25 = 0.12
Now, let's analyze if the values of the function increase or decrease as we go from -1 to 2 in the domain.
-1 < 0 < 1 < 2
We can see that as we increase the values of x from -1 to 2, the corresponding values of y = 15, 3, 0.6, 0.12 continuously decrease. So in this case, the values of the function y = 3(1/5)^x decrease as the values of the domain increase.
I hope this explanation helps you understand how to evaluate the functions and analyze the trends of their values. Let me know if you have any further questions!