help i don't get these two questions!!
21.What is the range of f(x) = |x + 2| + 3?
Option A: y is less than -2
Option B: y is less than 3
Option C: y is greater than -2
Option D: y is greater than three
30.What are the coordinates of the vertex of the graph of f(x) = 2|x| + 4?
(2, 4)
(0, 4)
(2, 0)
(4, 2)
i think for question 30 it is 0,4 am i correct?? and can u plz help me with the other question???
nvm i figured both problems out
Hi Mary,
Q30 : Yes you are correct. Vertex is the highest point of a graph. Moreover,the f(x) cannot be zero because if f(x) = 0,
then 2|x| = -4
|x| = -2 ,which is undefined since |x|is always positive.
Q21 : The answer is D. Try to substitute a number of x value and you'll get to see the pattern. The least value of y is 3.
Hope my explanation helps :)
Sure, I can help you with those two questions!
For the first question, to find the range of the function f(x) = |x + 2| + 3, we need to determine the possible values of the function output (y-values). One way to do this is by analyzing the behavior of the absolute value function.
The function f(x) = |x + 2| + 3 represents the absolute value of (x + 2) with 3 added to each value. The absolute value function always produces non-negative values, meaning it can never be less than zero.
So, to find the range, we need to look for the minimum value of the function. Since the absolute value function always outputs zero or a positive value, the lowest possible value of f(x) is when the absolute value expression (x + 2) = 0. Solving for x, we get x = -2.
Plugging x = -2 back into the function, we find f(-2) = |-2 + 2| + 3 = 0 + 3 = 3. Therefore, the minimum value of f(x) is 3, and any value greater than or equal to 3 is in the range of f(x).
Now looking at the options:
Option A: y is less than -2 - This is not correct because the function never goes below 3.
Option B: y is less than 3 - This is not correct either because the function starts at 3 and can go higher.
Option C: y is greater than -2 - This is correct since the range includes values greater than -2.
Option D: y is greater than 3 - This is not correct because the range starts at 3.
Therefore, the correct answer for the range of f(x) = |x + 2| + 3 is option C: y is greater than -2.
Moving on to the second question, we need to find the coordinates of the vertex of the graph of f(x) = 2|x| + 4. The vertex represents the point where the graph reaches its minimum or maximum value. In this case, since the coefficient of the absolute value is positive, the vertex will be the minimum point, and the graph opens upwards.
When an absolute value function is in the form f(x) = a|x - h| + k, the vertex has coordinates (h, k).
In our function f(x) = 2|x| + 4, a = 2, h = 0, and k = 4. Plugging these values into the vertex formula, we have (h, k) = (0, 4).
Therefore, the correct answer for the coordinates of the vertex of the graph of f(x) = 2|x| + 4 is (0, 4).