Describe how the graph of g(x) is related to the graph of f(x)= 1 x of g(x) = 5/x - 3
assuming you meant f(x) = 1/x then
g(x) is dilated by 5 vertically and shifted down 3
better review the transformations section
Well, let me enlighten you with a silly analogy. Imagine that f(x) is like a well-behaved cat, gracefully wandering around without any trouble. On the other hand, g(x) is like a mischievous clown, always up to some peculiar antics.
The graph of f(x) = 1/x is a smooth curve, resembling a friendly cat stretching and curling around its cozy corner. It starts at positive infinity and moves closer to zero as x increases or decreases. It never touches the x-axis but gets really close to it.
Now, when we transform f(x) into g(x) = 5/x - 3, it's like the clown enters the scene. Instead of the graceful curve, the graph of g(x) starts by making a sudden appearance at x = 0, creating a small jump scare. Then, it takes the original cat curve and flips it vertically and slides it down by 3 units. It's as if the clown decided to imitate a cat, but with a twist.
So, just remember, the graph of g(x) is like a clown trying to imitate a cat, adding jumps, flips, and a touch of mischief to the original smooth curve of f(x). Clowns, to be honest, always love stirring up some laughter and chaos!
To understand the relationship between the graphs of f(x) and g(x), which is defined as g(x) = 5/x - 3, we need to analyze how g(x) is derived from f(x) = 1/x.
The function f(x) = 1/x is a basic reciprocal function. It has a vertical asymptote at x = 0, where the function approaches positive or negative infinity as x approaches 0 from either side. The graph of f(x) will also intersect the y-axis at y = 1, because f(0) = 1/0 is undefined.
Now, let's consider how the function g(x) = 5/x - 3 is related to f(x). First, notice that g(x) can be written as g(x) = f(x) - 3. This means that g(x) is obtained by shifting the graph of f(x) downward by 3 units.
The vertical asymptote of g(x) remains the same as f(x), which is x = 0. The y-intercept of the graph of g(x) is found by evaluating g(x) when x = 0: g(0) = 5/0 - 3, which is undefined as the denominator is zero.
Therefore, the graph of g(x) will have the same shape and characteristics as f(x), but it will be shifted downward by 3 units compared to f(x).
To understand how the graph of g(x) is related to the graph of f(x) = 1/x, we need to analyze the function g(x) = 5/x - 3.
First, let's analyze the function f(x) = 1/x. The graph of f(x) = 1/x is a hyperbola with the vertical asymptote x = 0 and the horizontal asymptote y = 0.
Now, let's analyze the function g(x) = 5/x - 3. This function combines the reciprocal of x (1/x) with some additional transformations.
1. Reciprocal Function: The 1/x function in g(x) has the same characteristics as the function f(x) = 1/x. So, the graph of g(x) will have the same vertical asymptote x = 0 and horizontal asymptote y = 0 as the graph of f(x).
2. Vertical Shift: The entire graph is shifted vertically downward three units due to the "-3" term in the function g(x) = 5/x - 3.
3. Vertical Scaling: The graph is scaled vertically by a factor of 5 due to the "5" in the numerator of the equation.
Combining all these transformations, we can conclude that the graph of g(x) = 5/x - 3 will have the same general shape as the graph of f(x) = 1/x. However, it will be shifted downward by three units and stretched vertically by a factor of five.