For the following function find f(-2.9) and f(0)
f(x)={(2x+7, -5<=x<-3),(-(3)/(4)(x+2)^(2)+3, -3<=x<0),(2\log _(5)(x+1)-2, 0<=x<4)}
Answer choices:
f(-2.9)= 1.2 and f(0)= 0
f(-2.9)= 1.2 and f(0)= -2
f(-2.9)= 2.3925 and f(0)= 0
f(-2.9)= 2.3925 and f(0)= -2
Im thinkin its B but I really just guessed I dont know whats going on
although this is old, for anyone struggling i will explain it and give the answer because i struggled a bit too until i watched a video on it!
to find f(-2.9) you're going to have to find where -2.9 lies in the inequalities.
we have -5<=x<3, -3<=x<0, and 0<=x<4. -2.9 lies in -3<=x<0 and the function matching with those inequalities is f(x)= -3/4(x+2)^2+3. plug in -2.9 for x and you will get f(-2.9)= 2.3925.
do the same with 0. the function you will plug in 0 to is f(x)= 2log_5(x+1)-2. you will get f(0)= -2.
so TL;DR, f(-2.9)= 2.3925 and f(0)= -2
hope this helps!!<3
Well, let's figure it out together! Don't worry, I won't let you down!
For the function f(x), we need to look at the different ranges for x and evaluate the function accordingly.
First, let's check the range -5 <= x < -3. According to the function, f(x) = 2x + 7 in this range. So, for f(-2.9):
f(-2.9) = 2(-2.9) + 7
f(-2.9) = -5.8 + 7
f(-2.9) ≈ 1.2
Good job! Now, let's move on to the next range, -3 <= x < 0. In this range, f(x) = (-3/4)(x+2)^2 + 3. So, for f(0):
f(0) = (-3/4)(0+2)^2 + 3
f(0) = (-3/4)(2)^2 + 3
f(0) = (-3/4)(4) + 3
f(0) = -12/4 + 3
f(0) = -3 + 3
f(0) = 0
Now, let's check if our calculations match any of the answer choices:
A. f(-2.9) = 1.2 and f(0) = 0: Correct!
B. f(-2.9) = 1.2 and f(0) = -2: Nope, different from our calculations.
C. f(-2.9) = 2.3925 and f(0) = 0: Nope, doesn't match our calculations either.
D. f(-2.9) = 2.3925 and f(0) = -2: Nope, not what we found.
So, the correct answer is A. f(-2.9) = 1.2 and f(0) = 0. Great job with your guess!
To find the values of f(-2.9) and f(0), we need to determine which rule in the given function definition applies to each input.
For f(-2.9), we look at the first rule: f(x) = (2x + 7, -5 <= x < -3). Since -5 <= -2.9 < -3, we can use this rule. Plugging in -2.9 for x, we get:
f(-2.9) = 2(-2.9) + 7 = -5.8 + 7 = 1.2.
For f(0), we look at the second rule: f(x) = (-(3/4)(x+2)^2 + 3, -3 <= x < 0). Since -3 <= 0 < 3, we can use this rule. Plugging in 0 for x, we get:
f(0) = -(3/4)(0+2)^2 + 3 = -(3/4)(2)^2 + 3 = -(3/4)(4) + 3 = -3 + 3 = 0.
Therefore, the correct answer is:
f(-2.9) = 1.2 and f(0) = 0. So, the answer choice is: f(-2.9)= 1.2 and f(0)= 0
To find the values of f(-2.9) and f(0) for the given function, we need to evaluate the function for the respective input values.
Let's break down the function and evaluate each part for the given input values.
1. First, we need to determine which equation to use for each input value based on the given intervals.
For f(-2.9):
The given interval -5 <= x < -3 matches the condition, so we will use the equation (2x + 7) for this input.
For f(0):
The given interval 0 <= x < 4 matches the condition, so we will use the equation (2log5(x + 1) - 2) for this input.
2. Evaluating the function for f(-2.9):
Using the equation (2x + 7), substitute x = -2.9:
f(-2.9) = 2(-2.9) + 7 = -5.8 + 7 = 1.2
Therefore, f(-2.9) = 1.2.
3. Evaluating the function for f(0):
Using the equation (2log5(x + 1) - 2), substitute x = 0:
f(0) = 2log5(0 + 1) - 2 = 2log5(1) - 2 = 2(0) - 2 = -2
Therefore, f(0) = -2.
Now, comparing the calculated values to the answer choices provided, we find that f(-2.9) = 1.2 and f(0) = -2, which matches option D:
f(-2.9) = 1.2 and f(0) = -2
Hence, the correct answer is option D.