kyla
The point (-4, 7) is on the graph of y = f(x). What are its coordinates after a reflection across the y-axis?
(4, 7)
If a point (x, y) transforms to (x, -y), which reflection has occurred?
Reflection in the x-axis
If y = f(x) becomes y = 0.5f(3x), what are the vertical and horizontal transformations?
Vertical compression by a factor of 0.5 and horizontal compression by a factor of 1/3.
For y = f(bx), which value of 'b' would result in a horizontal compression?
b = 3
A point (2, 5) on the graph of y = f(x) is reflected across the x-axis. What are the new coordinates of this point?
(2, -5)
If the equation of a function changes from y = f(x) to y + 1 = f(x - 4), describe the translations.
Shift 4 units to the right and 1 unit down.
The transformation of y = f(x) to y = -f(x) causes which type of reflection?
Reflection across the x-axis
A graph of y = f(x) is shifted 2 units downwards. Which modification to y in the function's equation (y - k = f(x - h) form) represents this translation?
y + 2
Describe the vertical translation of the graph of y = f(x) if its equation becomes y - 6 = f(x).
Vertical shift 6 units up.
What happens to the coordinates (x, y) when a function is reflected across the x-axis?
(x, -y)
The graph of y = f(x) is translated 3 units to the left and 5 units down. What is the new equation?
y + 5 = f(x + 3)
Which equation represents a reflection of y = f(x) across the x-axis?
y = -f(x)
For y = af(x), which value of 'a' would result in a vertical stretch?
a = 2
Which equation shows a vertical compression of y = f(x)?
y = 0.5f(x)
If k < 0 in the translation equation y - k = f(x - h), how does this affect the graph vertically?
The graph shifts downwards.
How do the coordinates (x, y) change when a function is reflected across the y-axis?
(-x, y)
The graph of y = f(x) is transformed to y = f(x + 3). What is the effect of this transformation?
Horizontal shift 3 units to the left
A translation represented by h < 0 in y - k = f(x - h) results in which movement of the graph?
Horizontal shift to the left
Describe the reflection that transforms y = f(x) into y = f(-x).
Reflection across the y-axis.
If b > 1 in the equation y = f(bx), how does this affect the x-coordinates of the graph?
The x-coordinates are divided by b.
Describe the transformation y = f(x/3) applied to y = f(x).
Horizontal stretch by a factor of 3.
What is the effect on the graph of y = f(x) when x is replaced by (x + 3)?
Horizontal shift 3 units to the left.
Which equation represents a reflection of y = f(x) across the y-axis?
y = f(-x)
The function y = f(x) is transformed to y = 3f(x/2). Describe the transformations.
Vertical stretch, horizontal stretch
If y = f(x) is transformed to y = 4f(x/2), what is the combined effect on a point (x, y)?
(2x, 4y)
Describe the transformation if f(x) becomes f(x) - 5.
Vertical shift 5 units down.
A point (4, 6) is on the graph of y = f(x). After the transformation y = 2f(x/2), what are the new coordinates?
(8, 12)
A graph of y = f(x) is shifted 5 units to the right. Which modification to x in the function represents this translation?
x - 5
A graph is transformed such that a point (x, y) becomes (-x, y). What kind of transformation is this?
Reflection across the y-axis.
If a > 1 in the equation y = af(x), what effect does this have on the y-coordinates of the graph?
The y-coordinates are multiplied by a.
A vertical stretch by a factor of 4 transforms the point (x, y) to what?
(x, 4y)
How would the equation y = f(x) change if it were translated 8 units right?
y = f(x - 8)
Which equation represents a horizontal stretch by a factor of 2?
y = f(x/2)
Does reflecting y = f(x) across the x-axis change the sign of the x-coordinates?
No.
If y = f(x) becomes y = 3f(x), what transformation occurs?
Vertical stretch
If the graph of y = f(x) contains the point (-1, 0), what is the corresponding point on y = -f(x)?
(-1, 0)
What transformation does the equation y = f(-x) represent?
Reflection across the y-axis.
Describe the effect of 'b = 0.5' in the equation y = af(bx).
Horizontal stretch by a factor of 2.
How does the equation change when reflecting y = f(x) across the y-axis?
y = f(-x)
Describe the translation of y = f(x) to y - 5 = f(x + 1).
5 units up and 1 unit left.
A negative sign outside the function, as in y = -f(x), causes what effect?
Vertical flip over the x-axis
The equation y + 3 = f(x) represents which vertical translation?
3 units downwards
A point (4, 6) is transformed by y = f(2x). What are its new coordinates?
(2, 6)
The equation y = -f(x) results in which type of coordinate change?
y-coordinate sign changes
Which equation represents a function shifted 3 units right and 2 units down?
y + 2 = f(x - 3)
What is the specific effect on the x-coordinates when reflecting across the y-axis?
The x-coordinate changes its sign.
Which equation represents a reflection of y = f(x) across the x-axis?
y = -f(x)
If a point (5, -2) is reflected across the y-axis, what are its new coordinates?
(-5, -2)
Write the equation for reflecting y = x^2 across the x-axis.
y = -x^2
If a graph is shifted 6 units up, how is the 'k' value affected in the equation y - k = f(x - h)?
The value of k is 6.
Given y = f(x), what is the equation after translating 5 units left and 1 unit up?
y - 1 = f(x + 5)
If the equation y - k = f(x - h) has h = -2 and k = -4, describe the translation.
2 units left and 4 units down.
In y = af(bx), what value of 'a' would cause a vertical compression?
a = 1/2
What are the new coordinates if the point (2, 3) is translated 4 units left and 2 units down?
(-2, 1)
If a point (10, 5) is transformed by y = (1/5)f(x/2), what are its new coordinates?
(20, 1)
Write the equation for a vertical stretch by factor 5 and a horizontal compression by factor 1/2 for y = f(x).
y = 5f(2x)
A positive value of 'h' in y - k = f(x - h) indicates which type of translation?
A shift to the right
Which statement correctly describes the effect of k < 0 in y - k = f(x - h)?
The graph shifts downwards.
What is the effect of 'b > 1' on the graph of y = af(bx)?
Horizontal compression
In y = af(bx), if a = 1/3 and b = 4, describe the two transformations.
Vertical compression by a factor of 1/3 and horizontal compression by a factor of 1/4.