If a function f(x) is shifted to the left one unit, what function represents the transformation?
The function representing the transformation is f(x + 1).
Let g(x) be the reflection of f(x) = x² + 5 in the x-axis. What is a function rule for g(x)?
The function rule for g(x) is g(x) = -x² - 5.
What transformations change the graph of f(x) to the graph of g(x)?
f(x) = –7x² g(x) = –35x² + 5
The transformations that change the graph of f(x) to the graph of g(x) are:
1. A vertical stretch by a factor of 5.
2. A reflection in the x-axis.
3. A vertical translation upwards by 5 units.
Write an equation for the following transformation of y = x: a vertical stretch by a factor of 6.
The equation for the transformation of y = x, a vertical stretch by a factor of 6, would be y = 6x.
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
The transformations that change the graph of f(x) = x^2 to the graph of g(x) = (x + 3)^2 - 7 are:
1. A horizontal shift to the left by 3 units.
2. A vertical shift downwards by 7 units.
Note: The equation (x + 3)^2 represents a horizontal shift to the left by 3 units, while the -7 represents a vertical shift downwards by 7 units.
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
(1 point)
Responses
The graph of g is the graph of f translated to the right 3 units and up 7 units.
The graph of g is the graph of f translated to the right 3 units and up 7 units.
The graph of g is the graph of f translated to the left 3 units and down 7 units.
The graph of g is the graph of f translated to the left 3 units and down 7 units.
The graph of g is the graph of f translated up 3 units and to the left 7 units.
The graph of g is the graph of f translated up 3 units and to the left 7 units.
The graph of g is the graph of f translated down 3 units and to the right 7 units.
The graph of g is the graph of f translated down 3 units and to the right 7 units.
The graph of g is the graph of f translated to the left 3 units and down 7 units.
What is the graph of the inequality?
3x + 2y > –5
(1 point)
Responses
graphThe shaded region is to the left of a line that passes through the points left-parenthesis negative 5 comma 5 right-parenthesis, left-parenthesis negative 1 comma 0 right-parenthesis and left-parenthesis 3 comma negative 7 right-parenthesis.
Image with alt text: graph The shaded region is to the left of a line that passes through the points left-parenthesis negative 5 comma 5 right-parenthesis, left-parenthesis negative 1 comma 0 right-parenthesis and left-parenthesis 3 comma negative 7 right-parenthesis.
graphThe shaded region is to the right of a line that passes through the points left-parenthesis negative 5 comma 5 right-parenthesis, left-parenthesis negative 1 comma 0 right-parenthesis and left-parenthesis 3 comma negative 7 right-parenthesis.
Image with alt text: graph The shaded region is to the right of a line that passes through the points left-parenthesis negative 5 comma 5 right-parenthesis, left-parenthesis negative 1 comma 0 right-parenthesis and left-parenthesis 3 comma negative 7 right-parenthesis.
graphThe shaded area is a region to the left of a line that passes through the following points: left-parenthesis negative 2 comma negative 6 right-parenthesis, left-parenthesis negative 1 comma negative 4 right-parenthesis and left-parenthesis 6 comma 7 right-parenthesis.
Image with alt text: graph The shaded area is a region to the left of a line that passes through the following points: left-parenthesis negative 2 comma negative 6 right-parenthesis, left-parenthesis negative 1 comma negative 4 right-parenthesis and left-parenthesis 6 comma 7 right-parenthesis.
graph
The graph of the inequality 3x + 2y > -5 is the shaded region to the left of a line that passes through the points (-5, 5), (-1, 0), and (3, -7).
Image: graph The shaded region is to the left of a line that passes through the points (-5, 5), (-1, 0), and (3, -7).