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Resources

Find the vertex of the transformed function

Use the graphs of

f(x)

, shown in Figure

1

h(x)

, shown in Figure

2

, to evaluate the following expression.

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1

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2

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f(h(-1))=

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Identify the graph of

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g(x)=4x^{2}+24x+38

Graph the following function

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f(x)=-3 x-4

f(x)=\frac{4}{x^{2}-2 x-3}

is shown. For which values of

x

f(x)

Write an equation that represents the function graphed in blue by using transformations from

y=x^{2}

, which is graphed in green.

Make a table of solutions for the equation

y=x^{2}+3

. Then, choose the correct graph for the equation.

{:\left[\begin{array}{l}f(x)=-x^{

2

5

3

-f(x)\end{array}\right]:}

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f

g

are defined above. What is the value of

g(-1)

m

m(x)=10 x

n

n(x)=8 x-3

. Which of the following values of

x

satisfies the functional equation

m(x)-n(x)=7

h

h(x)=kx^{2}-7

h(5)=-57

, what is the value of

k

Which graph best represents

y=2x^{2}-5x-3

Using a double-angle or half-angle formula to simplify the given expressions.

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\cos ^{2}\left(22^{\circ}\right)-\sin ^{2}\left(22^{\circ}\right)=\cos \left(A^{\circ}\right)

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A=

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\square

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\cos ^{2}(9 x)-\sin ^{2}(9 x)=\cos (B)

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B=

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\square

Which type of conic section is defined by the equation

4 x^{2}-16 y^{2}+16 x-160 y-448=0

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This is an equation of

4

g(x)=f^{-1}(x)

f(x)=\sqrt{x-4}

g^{\prime}(1)

3

. Find the Maclaurin series generated by the function

f(x)=\frac{x^{2}}{1+x}

. Does this series converge at

x=1

Given the cell reaction:

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\mathrm{Ca}_{(\mathrm{s})}+\mathrm{Mg}^{2+}{ }_{(\mathrm{aq})} \leftrightarrows \mathrm{Ca}^{2+}{ }_{(\mathrm{aq})}+\mathrm{Mg}_{(\mathrm{s})}

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Which substance is oxidized?

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1

\mathrm{Ca}_{(s)}

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2

\mathrm{Mg}^{2+}{ }_{(a q)}

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3

\mathrm{Ca}^{2+}{ }_{(a q)}

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4

\mathrm{Mg}_{(\mathrm{s})}

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1

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2

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3

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4

\begin{array}{l}-\frac{1}{2} z^{3}=-108 \\ z=\square\end{array}

x(1400 x+6)+2(2 x+4)

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The expression shown above can be expressed as

c x^{2}+k x+m

c, k

, and mare constants. What is the value of

k

f

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

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x

-coordinate of the point on the function's graph that is closest to the origin?

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Choose all answers that apply:

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-\frac{\sqrt{3}}{3}

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-\frac{\sqrt{2}}{2}

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0

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\frac{\sqrt{3}}{3}

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\frac{\sqrt{2}}{2}

What is the inverse of the function

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g(x)=\frac{x^{3}}{8}+16

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g^{-1}(x)=\frac{\sqrt[3]{x-16}}{2}

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g^{-1}(x)=2\sqrt[3]{x}-16

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g^{-1}(x)=2\sqrt[3]{x+16}

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g^{-1}(x)=2\sqrt[3]{x-16}

What is the inverse of the function

g(x)=\frac{x^{3}}{8}+16

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\begin{array}{l} g^{-1}(x)=\frac{\sqrt[3]{x-16}}{2} \\ g^{-1}(x)=2 \sqrt[3]{x}-16 \\ g^{-1}(x)=2 \sqrt[3]{x+16} \\ g^{-1}(x)=2 \sqrt[3]{x-16} \end{array}

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f(x)=\left\{\begin{array}{cl}-\frac{1}{2} x-4 & \text { if } x<-1 \\ (x-2)^{2} & \text { if }-1 \leq x<3 \\ |x-5|-3 & \text { if } x \geq 3\end{array}\right.

r=\sqrt{x^{2}+y^{2}}

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The equation gives the quantity

r

in terms of the quantities

x

y

. Which of the following equations gives a possible value of

x

r

y

Deltal'ath Studen: Application

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Graph the equation shown below by transforming the given graph of the parent function

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y=\frac{1}{2} \cdot 2^{x}

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The graph shown could represent which of the following equ

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1

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h=-(b-10)(b-20)(b+20)

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h=(b-10)(b-20)(b+20)

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h=-(b+10)(b-20)(b+20)

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h=(b+10)(b-20)(b+20)

The polynomial function

f

f(m)=\left(m^{3}-m^{2}-17 m-15\right)(m+1)

f(m)

(m+1)

, what is the remainder?

5

pts) Describe how the graph of

g(x)=-\left(8 x^{-7}\right)+3

is related to the graph of

f(x)=8^{x}

x=\frac{1}{\sqrt{2}+\sqrt{3}}

, find the value of

x^{2}+\frac{1}{x^{2}}

1

The diagram below shows part of a straight line graph drawn to represent the equation

y=h a^{x}

h

a

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1

5

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Find the value of

h

a

y=-(x+3)^2 +4

is shown in the

xy

-plane. Which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?

If the function is one-to-one, list the inverse function

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\mathrm{f}=\{(-9,2),(9,-2),(-5,0),(5,0)\}

Given the function

f(x)=1-3 x^{2}

f(x)-3

as a simplified polynomial?

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Given the equation

n=\frac{\sin (\theta+\alpha)}{\sin \theta}

\alpha=45^{\circ}

, then an equivalent expression for

n

y=-3 x+4

f

f(x)=a x^{2}+b x+c

a, b

c

are constants and

1<a<4

y=f(x)

x y

-plane passes through points.

(11,0)

(-2,0)

a

is an integer, what could be the value of

a+b

Draw a graph of the equation for the line

y=3x^2-7

(b) Describe fully a sequence of transformations which transform the graph of

y=\frac{2}{x^{2}-1}

to the graph of

y=6+\frac{4}{4 x^{2}-1}

y=-\frac{1}{2}x^{2}-9

is graphed in the

xy

-plane, which of the following characteristics of the graph are displayed as a constant or coefficient in the equation?

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x

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y

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y

-coordinate of the vertex

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1

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(C) I and II only

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(D) II and III only

(A) The functions

g

h

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\begin{array}{l} g(x)=\log _{4}(2 x) \\ h(x)=\frac{\left(e^{x}\right)^{5}}{e^{1 / 4}} \end{array}

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g(x)=3

x

in the domain of

g

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h(x)=e^{1 / 2}

x

in the domain of

h

The graph of the polynomial equation

y=\alpha(t)

is shown. Which of the following must be true?

y=j(x)

y=k(x)

are shown. Which of the following graphs is the graph of

y=j(k(x))

Which graph represents the function of

f(x)=\frac{4 x^{2}-4 x-8}{2 x+2} ?

H D K N

H^{\prime} D^{\prime} K^{\prime} N^{\prime}

are shown on the coordinate grid where quadrilateral

H^{\prime} D^{\prime} K^{\prime} N^{\prime}

is a transformation of quadrilateral

H D K N

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Which algebraic description describes the transformation?

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(x, y) \rightarrow(x-5, y-3)

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\quad(x, y) \rightarrow(x-2, y-2)

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(x, y) \rightarrow(x+2, y+2)

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\quad(x, y) \rightarrow(x+5, y+3)

The figure shows the graph of

y=3x+33

. Which of the following is one of the two solutions

(x,y)

to the system of equations formed by this line and the curve determined by

y =-3(x+10)^2+9

The system of equations represented by the graph in the

x y

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y=x^{2}

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y=-x^{2}+2

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y=x+2

s=(t+3)^{2}(t+2)(t+1)(t)(t-1)

is graphed on the

s t

-plane. What is the product of the unique

t

-intercepts of the graph?

13

C

has parametric equations

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x=\frac{t^{2}+5}{t^{2}+1} \quad y=\frac{4 t}{t^{2}+1}

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Show that all points on

C

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(x-3)^{2}+y^{2}=4

What is the effect on the graph of the function

f(x)=x^{2}

f(x)

f(x)+

9

We are given that

\frac{d y}{d x}=x^{2}-2 y

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Fasind an expression for

\frac{d^{2} y}{d x^{2}}

x

y

\newline

\frac{d^{2} y}{d x^{2}}=

We are given that

\frac{d y}{d x}=e^{5 y}

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Find an expression for

\frac{d^{2} y}{d x^{2}}

x

y

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\frac{d^{2} y}{d x^{2}}=\square \text { I } \overline{+}

xy

-plane shows the graph of the quadratic equation

y=-(\frac{1}{4})(x-3)^2+2

. Which of the following represents all solutions

(x,y)

to the system of equations created by this quadratic equation and the linear equation

y=\frac{1}{2}(x+3)-7

...