f(x) =
{−8 if −3 ≤ x ≤ 0
{x if 0 < x ≤ 3
Evaluate the given expressions.
a)f(-1)=
b)f(0)=
(^Teach how to do this.)
What is the formula?
a)(−8)*(x > −3)*(x >= 0) + (x)*(x <= 0)*(x > 3)
b)(−8)*(x >= −3)*(x <= 0) + (x)*(x > 0)*(x <= 3)
c) (−8)*(x <= 0) + (x)*(x <= 3)
d)(−8)*(x >= −3) + (x)*(x > 0)
Thank You.
a. You have to be kidding. is -1 in the region -3 to 0? If so, f(-1)=-8
Now, which region is x=0 in?
b. second question on formula. All that makes no sense to me.
I like answer B
To evaluate the given expressions, we need to substitute the given values of x into the function f(x) and simplify the expression.
a) To find f(-1), we substitute x = -1 into the formula:
f(-1) = (-8)*(x > -3)*(x >= 0) + (x)*(x <= 0)*(x > 3)
Now, let's evaluate each part of the formula step by step:
(x > -3) evaluates to true because -1 is greater than -3.
(x >= 0) evaluates to false because -1 is not greater than or equal to 0.
(x <= 0) evaluates to true because -1 is less than or equal to 0.
(x > 3) evaluates to false because -1 is not greater than 3.
Now, substituting these evaluations into the formula:
f(-1) = (-8)*(true)*(false) + (-1)*(true)*(false)
Since false is equivalent to 0 and true is equivalent to 1, we can simplify the expression further:
f(-1) = 0 + 0 = 0
Therefore, f(-1) equals 0.
b) To find f(0), we substitute x = 0 into the formula:
f(0) = (-8)*(x >= -3)*(x <= 0) + (x)*(x > 0)*(x <= 3)
Evaluating each part of the formula:
(x >= -3) evaluates to true because 0 is greater than or equal to -3.
(x <= 0) evaluates to true because 0 is less than or equal to 0.
(x > 0) evaluates to false because 0 is not greater than 0.
(x <= 3) evaluates to true because 0 is less than or equal to 3.
Now, substituting these evaluations into the formula:
f(0) = (-8)*(true)*(true) + (0)*(false)*(true)
Simplifying the expression further:
f(0) = -8 + 0 = -8
Therefore, f(0) equals -8.
So the answers to the given expressions are:
a) f(-1) = 0
b) f(0) = -8
The correct formula for this function is option b) (−8)*(x >= −3)*(x <= 0) + (x)*(x > 0)*(x <= 3).