match the characteristic on the left to the function that has the same on the right.
1. rate of change -2
2. initial value of 5/
3. rate of change of 3
4. y-intercept of 7
an=3+(n-1)(-2), f(x)=3x-2, an=5+(n-1)(7)
1. rate of change -2 - an=3+(n-1)(-2)
2. initial value of 5/ - f(x)=3x-2
3. rate of change of 3 - an=5+(n-1)(7)
4. y-intercept of 7 - f(x)=3x-2
is this correct?
Apologies for the confusion. Let me correct my response:
1. rate of change -2 - an=3+(n-1)(-2)
2. initial value of 5/ - f(x)=3x+5/ (assuming you meant initial value of 5)
3. rate of change of 3 - an=5+(n-1)(7)
4. y-intercept of 7 - f(x)=7x (assuming you meant y-intercept of 7)
Again, apologies for any confusion caused.
To match the given characteristics to the functions, we need to understand what each characteristic represents and then compare it to the given functions:
1. Rate of change -2:
The rate of change represents how the function's output values (y-values) change with respect to the input values (x-values). A rate of change of -2 means that for every unit increase in the input value, the output value decreases by 2.
Looking at the given functions, we find that "an = 3 + (n-1)(-2)" matches the characteristic of a rate of change of -2. Thus, the answer for this characteristic is the function "an = 3 + (n-1)(-2)."
2. Initial value of 5:
The initial value, also known as the y-intercept, represents the value of the function when the input is 0, or the starting point of the function on the y-axis.
Observing the given functions, we see that "f(x) = 3x - 2" matches the characteristic of having an initial value of 5. Therefore, the answer for this characteristic is the function "f(x) = 3x - 2."
3. Rate of change of 3:
Similar to the first characteristic, a rate of change of 3 means that for every unit increase in the input value, the output value increases by 3.
None of the given functions match the characteristic of a rate of change of 3. Therefore, none of the functions can be matched with this characteristic.
4. Y-intercept of 7:
The y-intercept, as mentioned above, represents the value of the function when the input is 0. In this case, it is specifically stated as a y-intercept of 7.
Looking at the given functions, we find that "an = 5 + (n-1)(7)" matches the characteristic of a y-intercept of 7. Hence, the answer for this characteristic is the function "an = 5 + (n-1)(7)."
So, to summarize the matching:
1. Rate of change -2 - Function: an = 3 + (n-1)(-2)
2. Initial value of 5 - Function: f(x) = 3x - 2
3. Rate of change of 3 - No matching function
4. Y-intercept of 7 - Function: an = 5 + (n-1)(7)