Edmentum Integrated Math1 Unit3 Linear Function Transformations

00:00 Tutorial
32:29 Practice
55:36 Mastery Test

Consider the function f(x) = 3x + 1 and the graph of the function g(x) shown below.

The function f(x) is shown on the provided graph.

Which statement describes the graph of function g?

f(x) = 2x
g(x) = 2x + 3

The graph of g is 3 units above the graph of f.
The graph of g is 3 units to the left of the graph of f.
The graph of g is 3 units below the graph of f.
The graph of g is 3 units to the right of the graph of f.

Each statement describes a transformation of the graph of y = x. Which statement correctly describes the graph of y = x + 7?

It is the graph of y = x translated 7 units to the right.
It is the graph of y = x translated 7 units up.
It is the graph of y = x translated 7 units down.
It is the graph of y = x where the slope is increased by 7.

Each statement describes a transformation of the graph of y = x. Which statement correctly describes the graph of y = x − 8?

It is the graph of y = x translated 8 units down.
It is the graph of y = x translated 8 units up.
It is the graph of y = x where the slope is decreased by 8.
It is the graph of y = x translated 8 units to the left.

Which transformation of f(x) will produce the same graph as g(x)?

f(x) = 3x
g(x) = f(x) + 3

h(x) = f(x − 1)
h(x) = 2f(x)
h(x) = f(x) + 1
h(x) = f(x + 1)

Which statement is true about the effects of the transformations on the graph of function f to obtain the graph of function g.

g(x) = f(x − 3) + 4

The graph of function f is shifted right 3 units and down 4 units.
The graph of function f is shifted left 3 units and up 4 units.
The graph of function f is shifted left 3 units and down 4 units.
The graph of function f is shifted right 3 units and up 4 units.

The graph of g is one-fifth as steep as the graph of f.
The graph of g is one-fifth of a unit to the right of the graph of f.
The graph of g is five times steeper than the graph of f.
The graph of g is one-fifth of a unit to the left of the graph of f.

Suppose the following function is graphed.

On the same grid, a new function is graphed. The new function is represented by the following equation.

Which of the following statements about these graphs is true?

The graphs intersect at (0,8).
The graph of the original function is perpendicular to the graph of the new function.
The graph of the original function is parallel to the graph of the new function.
The graphs intersect at (0,4).

If the graph of function g is 6 units below the graph of function f, which could be function g?

f(x) = -2x + 7

g(x) = -2x + 20
g(x) = -2x − 6
g(x) = -2x + 1
g(x) = -6x + 7

Each statement describes a transformation of the graph of y = x. Which statement correctly describes the graph of y = x + 9.5?

It is the graph of y = x translated 9.5 units down.
It is the graph of y = x translated 9.5 units to the right.
It is the graph of y = x where the slope is increased by 9.5.
It is the graph of y = x translated 9.5 units up.

Each statement describes a transformation of the graph of y = x. Which statement correctly describes the graph of y = x − 13?

It is the graph of y = x translated 13 units to the left.
It is the graph of y = x where the slope is decreased by 13.
It is the graph of y = x translated 13 units to the right.
It is the graph of y = x translated 13 units up.

In the function above, the slope will be multiplied by -9, and the y-value of the y-intercept will be increased by 2 units. Which of the following graphs best represents the new function?

In the function above, the slope will be multiplied by -4, and the y-value of the y-intercept will be decreased by 1 unit. Which of the following graphs best represents the new function?

The slope of the function on the left is multiplied by p, and q is added to the y-intercept to arrive at the function on the right. Which of the following are the values for p and q?

Determine which sequences of transformations could be applied to the parent function, f(x) = x, to obtain the graph above.

Reflect over the x-axis, vertically stretch by a factor of 2, and then shift up 6 units
Reflect over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units
Shift right 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2
Shift left 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2
Shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2
Shift left 2 units, reflect over the y-axis, and then vertically stretch by a factor of 6

Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(x) + 7?

Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(x + 11)?

Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = 8f(x)?