What transformations change the graph of f left-parenthesis x right-parenthesis to the graph of g left-parenthesis x right-parenthesis?
f left parenthesis x right parenthesis equals x squared
g left parenthesis x right parenthesis equals left parenthesis x plus 3 right parenthesis squared minus 7
Responses:
a) The graph of g is the graph of f translated to the right 3 units and up 7 units.
b) The graph of g is the graph of f translated to the left 3 units and down 7 units.
c) The graph of g is the graph of f translated up 3 units and to the left 7 units.
d) The graph of g is the graph of f translated down 3 units and to the right 7 units.
The correct answer is a) The graph of g is the graph of f translated to the right 3 units and up 7 units.
In the transformation, we can see that x+3 in g(x) implies a translation to the right by 3 units, and -7 implies a translation up by 7 units.
Write an inequality for the graph.
y= 5
slope= 1
x= -6
responses:
a) –6x + 5y ≥ –30
b) –6x + 5y ≤ –30
c) 5x – 6y ≤ –30
d) 5x – 6y ≥ –30
The correct answer is d) 5x - 6y ≥ -30.
To determine the inequality for the graph, we can consider the given information.
First, y = 5 represents a horizontal line at y = 5. This means that all points on the line have a y-coordinate of 5.
Second, the slope is not relevant in this case since the line is horizontal and has a constant y-value of 5.
Third, x = -6 represents a vertical line at x = -6. This means that all points on the line have an x-coordinate of -6.
Combining these observations, we can say that all points on the graph satisfy x = -6 and y = 5. This can be written as the inequality 5x - 6y ≥ -30.