ACT 1 Geo: Identify transformations - One Minute Per Question

Welcome to your ACT 1 Geo: Identify transformations

$Q_{1}:$ Graphical transformations of functions fall into three categories expect?

Horizontal and Vertical shifts

Reflections

Around

The widening and narrowing

$Q_{2}:$ If $f(x)=x^{2}+2$ and $g(x)$ is a transformation of $f(x)$ when the graph is moved three units up and six units to the left, what is $g(x)$?

$g(x)=(x+6)^{2}+5$

$g(x)=(x+3)^{2}+8$

$g(x)=(x+5)^{2}+8$

$g(x)=(x+2)^{2}+9$

$Q_{3}:$ What is the equation of the circle shown below?

$(x-4)^{2}+(y-2)^{2}=9$

$(x+4)^{2}+(y+2)^{2}=9$

$(x-4)^{2}+(y-2)^{2}=36$

$(x+4)^{2}+(y+2)^{2}=36$

$Q_{4}$ In which quadrant(s) will the graph of the circle with equation $(x+8)^{2}+(y-15)^{2}=49$ be contained?

$I$ only

$II$ only

$II$ and $III$

$IV$ only

$Q_{5}:$ Which of the following equations represents a circle with center at $(-4,6)$ and a radius of $6$ units?

$(x-6)^{2}+(y-4)^{2}=9$

$(x-6)^{2}+(y-4)^{2}=36$

$(x+4)^{2}+(y-6)^{2}=9$

$(x-4)^{2}+(y+6)^{2}=9$

$Q_{6}:$ For equations in the form of $ax^{2}+ bx +c$, in algebraic change if $a>1$, then graphic result is:

Parabola becomes wider

Parabola becomes narrower

Reflection over the $x$-axis

Reflection over the $y$-axis

$Q_{7}:$ If $f(x) = 2x^{ 2} + 3x − 12$, what is $f(x − 4)$?

$ x^{2} - 13 x -16$

$ x^{2} - 12 x -16$

$2 x^{2} - 12 x -16$

$2 x^{2} - 13 x + 8$

$Q_{8}:$ The figure below is the graph of $f(x)$ in the $xy$-plane. The function $g$ is defined as $f(x − 2)$. At what value of $x$ is $g(x) = 3$?

$0$

$1$

$2$

$3$

$Q_{9}:$ If $f(x) = 7x + 3$ and $f(x − b) = 7x − 18$, what is the value of $b$?

$1$

$2$

$3$

$4$

$Q_{10}:$ Which type of transformation can be used to obtain the graph of $g(x) = 4(2^{x} )$ from the graph of $f(x) = 2^{x}$ ?

Vertical shrink

Vertical shift down

Vertical shift up

Vertical stretch

$Q_{11}:$ Parallelogram $ABCD$ was transformed to form parallelogram $A′B′C′D′$. Which rule describes the transformation that was used to form parallelogram $A′B′C′D′$?

$(x,-y)$

$(-x,y)$

$(x+6,-y)$

$(-x,y-3)$

$Q_{12}:$ The graph of the function $h$ was obtained from the graph of the function $g$ using a composite transformation, as shown below. Which equation can be used to describe $h(x)$ in terms of $g(x)$?

$h(x) = g(x + 4) + 2$

$h(x) = g(x + 4) - 2$

$h(x) = g(x - 4) - 2$

$h(x) = g(x - 4) + 2$

$Q_{13}:$ Which two transformations can be used to obtain the graph of $g(x) = -\sqrt{ x - c}$ from the graph of $f(x) =\sqrt{ x }$if $c > 0$?

A translation to the right $c$ units followed by a reflection across the $x$-axis.

A translation to the left $c$ units followed by a reflection across the $x$-axis.

A translation to the right $c$ units followed by a reflection across the $y$-axis.

A translation to the left $c$ units followed by a reflection across the $y$-axis.

$Q_{14}:$ For the functions $h$ and $g$, which statement is true if $h(x) = g(x + 14) − 12$?

The graph of $h$ is the result of the graph of $g$ being translated right $14$ units and down $12$ units.

The graph of $h$ is the result of the graph of $g$ being translated left $14$ units and down $12$ units.

The graph of $h$ is the result of the graph of $g$ being translated right $14$ units and up $12$ units.

The graph of $h$ is the result of the graph of $g$ being translated left $14$ units and up $12$ units.

$Q_{15}:$ A function is graphed below. Which function is best represented by this graph?

$ y = −(x + 1)^{2} + 4$

$ y = −(x - 1)^{2} + 4$

$ y = −x^{2} + 4x+3$

$ y = −x^{2} - 4x+3$

$Q_{16}:$ If $f(x) = x + 3$, then the line shown in the $xy$-plane below is the graph of?

$f(x) $

$f(x-6) $

$f(x-3) $

$f(x+6) $

$Q_{17}:$ If $f(x) = x^{ 2}$ , then the graph shown in the $xy$-plane below best represents which of the following functions?

$f(-x)$

$f(x-1)$

$f(x+1)$

$f(x^{ 2}-1)$

$Q_{18}:$ If $f(x) = 2x – 2$, then which of the following is the graph of $f(\frac{x-2}{2}) $?

$A$

$B$

$C$

$D$

$Q_{19}:$ If $f(x) = 2$, then the line shown in the $xy$-plane below ?

$f(x+1)$

$f(x-1)$

$f(x+2)$

All of the above

$Q_{20}:$ If $f(x) = (x – 1)^{ 2} + 1$, what is the $y$-intercept of the graph of $f(x+ 1)$ in the $xy$-plane?

$-2$

$-1$

$0$

$1$

$Q_{21}:$ If $f(y) = –(y^{2} + 1)$, then the graph shown in the $xy$-plane below best represents which of the following functions?

$f(-y)$

$f(y+1)$

$f(y-1)$

$f(y-2)$

$Q_{22}:$ In the $xy$-plane below, if the scales on both axes are the same, which of the following could be the equation of $l_{ 1}$ ?

$y=\frac{2}{3}x-3$

$y=-2x+1$

$y=3x-\frac{2}{3}$

$y=-\frac{2}{3}x-3$

$Q_{23}:$ If $f(x) = -\frac{1}{2}x$, then the line shown in the $xy$- plane below is the graph of?

$f(x)$

$f(x-3)$

$f(x+3)$

$f(-4x)$

$Q_{24}:$ If $f(x) = -2x ^{2} + 2$, then the graph shown in the $xy$-plane below best represents which of the following ?

$f(\frac{1}{2}x)$

$f(-\frac{1}{x})$

$f(\frac{x}{\sqrt{8}})$

$f(-\frac{x}{4})$

$Q_{25}:$ The graph of $y = f (x – r)$ where $r$ is a positive number is obtained by?

shifting the graph of $y = f (x)$, $r$ units to the RIGHT.

shifting the graph of $y = f (x)$, $r$ units to the LEFT.

reflecting the graph of $y = f (x)$ in the $ x$-axis.

shifting the graph of $y = f (x)$ DOWN $r$ units.

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