f(x) cannnot be a graph of itself translated down by anything other than 0 units.
graph gx is the reflection of graph fx and then transformed 1 unit down
y=x
at first draw the graph of fx, then shift the graph along -ve x-axis 21 unit
The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has been changed somewhat. Which of the following could be the equation of F(x)?
What is the area bounded by the graph of the function f(x)=1-e^-x over the interval [-1, 2]?
graph gx is the reflection of graph fx and then transformed 1 unit down
When the graph of a function ( f(x) ) is translated left or right by ( k ), the rule for the function changes by adjusting the input variable ( x ). Specifically, if the graph is translated to the right by ( k ), the new function becomes ( f(x - k) ). Conversely, if the graph is translated to the left by ( k ), the new function becomes ( f(x + k) ). This transformation shifts the entire graph horizontally without altering its shape.
y=x
False
at first draw the graph of fx, then shift the graph along -ve x-axis 21 unit
graph G(x)=[x]-1
The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has been changed somewhat. Which of the following could be the equation of F(x)?
The result depends on how the function f() is defined. Simply copy the function definition, replacing every "x" (assuming the function is defined in terms of "x") by "x+5".
The graph of the function f(x) = 4, is the horizontal line to the x=axis, which passes through (0, 4). The domain of f is all real numbers, and the range is 4.
True
What is the area bounded by the graph of the function f(x)=1-e^-x over the interval [-1, 2]?
Yes. It is a piece-wise function with the limit: lim{x->0}= 0 You graph both parts as two series of dotted lines since there are infinite rational and irrational possibilities