I Need Help ?
I'm Suppose to graph this and the domain and range,
How Do i find this ?
1) f(x)=x^2+4 ; x= -3, -2, -1, 0, 1, 2, 3
2)G(x)= squareroot of x+3 ; x= -3, -2, 1, 6
3.H(x)= |x|-4 ; x= -3,-2,-1,0,1,2,3
4.f(x)=4 ; x= -3,-2,-1,0,1,2,3
5.G(x)=x^3+1 ; x= -2,-1,0,1,2
plot the given points. For example, in #1, evaluate x^2+4 for each given x-value:
f(-3) = (-3)^2+4 = 9+4 = 13
and so on.
the graph sketch should help determine the range.
The domain of any polynomial is all reals.
squareroot(z) has domain z >= 0.
Is This the right range and domain for #1?
1. domain:(-0,0)
range: (4,0)
for problem 2 do i square root everything and then do the problem?
#1. You are almost correct, if you meant (-∞,∞) and [4,∞)
Foe #2, √(x+3) means you plot
(-3,0), (-2,1), (1,2), and (6,3)
domain: you need (x+3) >= 0, or x >= -3. That is, [-3,∞)
range: [0,∞)
Thank you!
and for problem 2 shouldn't it be 9?
I don't know for some reason i got 9.
and
Can you check these answers?
For problems 3,4,5
3.Domain:(-∞,∞)
Range:(0,∞)
4.Domain:(-∞,∞)
Range:y=4
5.Domain:(-∞,∞)
range:(-∞,∞)
#2: shouldn't *what* be 9?
#3: range of |x| is [0,∞), so the range of |x|-4 is [-4,∞)
#4: correct
#5: correct
Thanks Again!
and #2 when i pugged everything in i got 9 instead of 6.
I'm still lost on #2. What do you mean "plug everything in"?
where did I get 6? The only 6 I see is the last given value for x. √(6+3) = √9 = 3.
Show me your calculation. Saying you got 9 doesn't tell me how you got it.
To graph a function and find its domain and range, follow these steps:
Step 1: Understand the Function
First, you need to understand the given function. Look at the expression provided and identify what type of function it represents (quadratic, square root, absolute value, constant, etc.). This knowledge will help you determine the general shape and behavior of the function.
Step 2: Identify the Domain
The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. To find the domain, look at the given values of x. In some cases, like the ones you provided, the domain is explicitly stated. In other cases, you might need to consider any restrictions or limitations mentioned in the problem.
Step 3: Calculate the Range
The range of a function refers to the set of all possible output values (y-values) that the function can generate. To find the range, you can either graph the function and observe the vertical spread of the curve or use algebraic techniques to analyze the behavior of the function.
Step 4: Graph the Function
To graph the function, plot the given points using the x-values from the domain and their corresponding y-values obtained by substituting the x-values into the function. Connect the plotted points to form a smooth curve. If the given points are few, you can directly plot them. However, if there is a large set of points, you may need to use a graphing calculator, software, or online tools.
Now, let's apply these steps to your specific examples:
1) f(x) = x^2 + 4; x = -3, -2, -1, 0, 1, 2, 3
- The given function is a quadratic function.
- The domain is explicitly stated as x = -3, -2, -1, 0, 1, 2, 3.
- To find the corresponding range, substitute each x-value into the function and calculate the corresponding y-values.
- Plot the points (-3, 13), (-2, 8), (-1, 5), (0, 4), (1, 5), (2, 8), and (3, 13) on the coordinate plane.
- Connect the points to form a smooth curve.
2) G(x) = sqrt(x + 3); x = -3, -2, 1, 6
- The given function is a square root function.
- The domain is explicitly stated as x = -3, -2, 1, 6.
- To find the corresponding range, substitute each x-value into the function and calculate the corresponding y-values.
- Plot the points (-3, 0), (-2, 1), (1, 2), and (6, 3) on the coordinate plane.
- Connect the points to form a smooth curve.
3) H(x) = |x| - 4; x = -3, -2, -1, 0, 1, 2, 3
- The given function is an absolute value function.
- The domain is explicitly stated as x = -3, -2, -1, 0, 1, 2, 3.
- To find the corresponding range, substitute each x-value into the function and calculate the corresponding y-values.
- Plot the points (-3, -7), (-2, -6), (-1, -5), (0, -4), (1, -3), (2, -2), and (3, -1) on the coordinate plane.
- Connect the points to form a smooth v-shaped curve.
4) f(x) = 4; x = -3, -2, -1, 0, 1, 2, 3
- The given function is a constant function.
- Since the function is a horizontal line at y = 4, the range is y = 4 for all x-values.
- Plot the points (-3, 4), (-2, 4), (-1, 4), (0, 4), (1, 4), (2, 4), and (3, 4) on the coordinate plane. You will have a straight horizontal line passing through y = 4.
5) G(x) = x^3 + 1; x = -2, -1, 0, 1, 2
- The given function is a cubic function.
- The domain is explicitly stated as x = -2, -1, 0, 1, 2.
- To find the corresponding range, substitute each x-value into the function and calculate the corresponding y-values.
- Plot the points (-2, -7), (-1, 0), (0, 1), (1, 2), and (2, 9) on the coordinate plane.
- Connect the points to form a smooth curve.
Remember, these are just general steps to guide you in solving graphing problems and determining domain and range. Practice and understanding the properties of different types of functions will help you become more proficient in graphing and analyzing functions.