This is probably really easy but I am confused.
#1 Find the domain and graph the function:
f(x)= sq root x-1
#2 Graph the function g(x)=(x + 3)^3
Do you know what the parent functions of y = sqrt(x) and y = x^3 look like? The functions f and g are simply those parent functions with a horizontal shift.
You may not take the square root of a negative number
therefore x>/=1
well, go ahead pick some values of x and put the function on a graph. Note odd about the vertical line x = -3
Sure! Let's break it down step by step.
#1 Find the domain and graph the function f(x) = √(x-1):
Step 1: Determine the domain of the function. The domain is the set of all real numbers for which the function is defined. In this case, since we have a square root, the expression inside the square root (x-1) must be greater than or equal to 0, because we can't take the square root of a negative number. So, we set x-1 ≥ 0 and solve for x:
x - 1 ≥ 0
x ≥ 1
Therefore, the domain of the function is all real numbers greater than or equal to 1, or in interval notation, [1, ∞).
Step 2: Now let's graph the function. Start by plotting some key points.
Choose some x-values, for example, x = 1, 2, 3, 4, and find the corresponding y-values using the given function:
For x = 1:
f(1) = √(1-1) = √0 = 0
For x = 2:
f(2) = √(2-1) = √1 = 1
For x = 3:
f(3) = √(3-1) = √2 ≈ 1.414
For x = 4:
f(4) = √(4-1) = √3 ≈ 1.732
Now we can plot these points on a graph and connect them smoothly:
(1, 0) (2, 1) (3, 1.414) (4, 1.732)
o-------o------------o------------o
The graph of f(x) = √(x-1) starts at (1, 0) and continues upward as x increases.
#2 Graph the function g(x) = (x + 3)^3:
Step 1: To graph the function, identify some key points.
Choose some x-values, for example, x = -3, -2, -1, 0, and find the corresponding y-values using the given function:
For x = -3:
g(-3) = (-3 + 3)^3 = 0^3 = 0
For x = -2:
g(-2) = (-2 + 3)^3 = 1^3 = 1
For x = -1:
g(-1) = (-1 + 3)^3 = 2^3 = 8
For x = 0:
g(0) = (0 + 3)^3 = 3^3 = 27
Now we can plot these points on a graph and connect them smoothly:
(-3, 0) (-2, 1) (-1, 8) (0, 27)
o--------o---------o----------o
The graph of g(x) = (x + 3)^3 starts at (-3, 0) and continues upward as x increases.
No worries, I'm here to help! Let's break down each question step by step:
#1 Find the domain and graph the function:
To find the domain of a function, we need to determine the values of x that are valid inputs for the function. In this case, we have the function f(x) = √(x - 1).
The domain is the set of all real numbers for which the function is defined. Since we're dealing with a square root function, the value inside the square root (x - 1) must be non-negative, since the square root of a negative number is undefined in the real number system.
Therefore, we set the expression (x - 1) ≥ 0 to find the values of x that satisfy this condition. Solving this inequality, we get x ≥ 1.
So, the domain of the function f(x) = √(x - 1) is x ≥ 1, meaning all real numbers greater than or equal to 1 are valid inputs.
To graph the function, you can start by plotting a few points. Choose any values of x that satisfy the domain condition, such as x = 1, 2, 3, etc. Then, calculate the corresponding y-values using the function f(x) = √(x - 1). Connect the points and continue the graph to have a complete picture of the function.
#2 Graph the function g(x) = (x + 3)^3:
For this function, g(x) = (x + 3)^3, you can start by finding the critical points and the behavior of the function as x approaches positive and negative infinity.
There are no restrictions on the domain of a cubic function, so all real numbers are valid inputs.
To plot points, choose a few values of x and calculate the corresponding y-values by substituting those x-values into the given function. For example, if you choose x = -3, -2, -1, 0, 1, 2, etc., you can calculate the corresponding y-values for each x and plot the points.
Once you have enough points, connect them to create the graph of the function g(x) = (x + 3)^3. The graph will have a characteristic "S" shape due to the cubic power.