Given the Inequality Check all that apply. $$-2x-3\ge-11$$

The solution set for the linear inequality is $$x\le4$$

The interval notation that can be used to model the solution set is $$\left(-\infty,\ 4\right]$$

The solution set for the linear inequality is $$x\le8.5$$

The interval notation that can be used to model the solution set is $$\left(-\infty,-8.5\right]$$

Given the functions $$b\left(x\right)=\ \frac{2}{3}\left(x+1\right)$$ and $$t\left(x\right)=\ \frac{1}{2}\left(x+5\right)$$ Check all that apply.

b(x)<t(x) on the interval $$\left(-\infty,\ 11\right)$$

t(x) has a slope that is less than the slope of b(x)

b(x)<t(x) on the interval $$\left(11,\ \infty\right)$$

b(x) has a y-intercept that is greater than the y-intercept of t(x)

Given the inequality $$x^2+4x-43\le6x+5$$ . Check all that apply.

The solution set written in interval notation is [-6,8]

The solution set written as an inequality $$-6\le x\le8$$

The solution set written in interval notation is (-6,8)

The solution set written as an inequality $$-6

Given the functions $$g\left(x\right)=x^2+13$$ and $$t\left(x\right)=10x-8$$ .

Given g(x)>t(x) the interval notation used to model the solution set is $$\left(-\infty,3\right)U\left(7,\infty\right)$$

g(x) is a quadratic function and has a larger y-intercept than the linear function t(x)

Given g(x)>t(x) the interval notation used to model the solution set is $$\left(-\infty,2\right)U\left(7,\infty\right)$$

g(x) is a linear function and has a larger y-intercept than the quadratic function t(x)

Given the quadratic function $$g\left(x\right)=0.5\left(x-4\right)^2-3\ $$ , Check all that are true regarding the key features of g(x)

The point (4,-3) is the same as g(4)=-3 and is the minimum of the parabola

The point (4,-3) is the same as g(4)=-3 and is the maximum of the parabola

g(x) is positive on the interval (1.55, 6.45)

g(x) is negative on the interval $$\left(-\infty,1.55\right)U\left(6.45,\infty\right)$$

Given the quadratic function $$g\left(x\right)=0.5\left(x-4\right)^2-3\ $$ , Check all that are true regarding the key features of g(x)

g(x) is positive on the interval x<1.55 or 6.45<x

g(x) is increasing on the interval $$\left(4,\infty\right)$$

g(x) is increasing on the interval $$\left(-\infty,4\right)$$

Given the function $$h\left(x\right)=-\sqrt[]{x+5}+4$$ . Check all the statements that are true regarding the key features.

h(x) has an x-intercept of x=11

h(x) has an x-intercept of x=1.764

Given the function $$h\left(x\right)=-\sqrt[]{x+5}+4$$ . Check all the statements that are true regarding the key features.

The domain of the function h(x) is $$\left[-5,\infty\right)$$

The domain of the function h(x) is $$\left(-\infty,\infty\right)$$

The domain of the function h(x) is $$\left(-5,\ \infty\right)$$

The domain of the function h(x) is $$\left(-\infty,4\right]$$

Given the function $$h\left(x\right)=-\sqrt[]{x+5}+4$$ . Check all the statements that are true regarding the key features.

The is no interval in which h(x) is increasing

The function h(x) is negative on the interval $$\left(11,\infty\right)$$

The range of the function h(x) is $$\left(-\infty,4\right]$$

The interval of decrease for the function h(x) is $$\left[5,\infty\right)$$

Given the function $$h\left(x\right)=-\sqrt[]{x+5}+4$$ . Check all the statements that are true regarding the key features.

The end behavior for h(x) can be explained as the function will continue to decrease to negative infinite

Part of the end behavior for h(x) can be written as $$x\rightarrow\infty,\ \ y\rightarrow-\infty$$

Part of the end behavior for h(x) can be written as $$x\rightarrow\infty,\ \ y\rightarrow4$$

The end behavior for h(x) can be explained as the function will continue to decrease to the value x = 11 then it hits y = 0 and stops.

Given the function $$t\left(x\right)=\frac{4}{x+3}$$ . Check all that all that play

t(x) has a discontinuity/ vertcal asymptote at x=-3

t(x) has a discontinuity/ vertcal asymptote at x=3

The function t(x) is increasing on the interval $$\left(-\infty,\infty\right)$$ except -3

The function t(x) is increasing on the interval $$\left(-\infty,\infty\right)$$ except 3

Given the function $$t\left(x\right)=\frac{4}{x+3}$$ . Check all that all that play

The function t(x) is decreasing on the interval $$\left(-\infty,\infty\right)$$ except -3

The function t(x) is positive on the interval $$x>-3$$

The function t(x) is positive on the interval $$\left(-3,\infty\right)$$

The function t(x) is negative on the interval $$\left(-\infty,-3\right)$$

Given the function $$t\left(x\right)=\frac{4}{x+3}$$ . Check all that all that play

The function has end behavior in which the graph will approach the line y=0

The function has end behavior in that can be described by the statement $$x\rightarrow\infty\ ,\ \ y\rightarrow0$$

The function has end behavior in which the graph will approach the line y=4

The function has end behavior in that can be described by the statement $$x\rightarrow\infty\ ,\ \ y\rightarrow4$$

Given the function 2b(x-3)+4 indicate the transformations if b(x) is the parent function.

The function b(x) has been translated right 3

The function b(x) has been vertically stretched by a factor of 2.

The function b(x) has be translated up 3

The function b(x) has been vertically compressed by a factor of 2.

Given the function -t(x+3)-5 indicate the transformations if t(x) is the parent function.

The function t(x) has been translated left 3

The function t(x) has been reflected over the x-axis

The function t(x) has been translated down 5

The function t(x) has been vertically stretched by 3

Given the parent function $$f\left(x\right)=x^2$$ , check all that apply if f(x) is transformed to 3f(x+5)-2

The function is transformed to $$3\left(x+5\right)^2-2$$

The vertex of the transformed function is a minimum and located at (-5,-2)

The function is increasing on the interval x > -5

The function is transformed to $$3\left(x-2\right)^2+5$$

Given the parent function $$f\left(x\right)=\sqrt[]{x}$$ , check all that apply if f(x) is transformed to -1/2f(x-4)+5

The function is transformed to $$-\frac{1}{2}\sqrt[]{x-4}+5$$

The function is transformed to $$-\frac{1}{2}\sqrt[]{\left(x-4\right)+5}$$

The function f(x) has been translated left 4 and up 5

The function f(x) has been translated right 4 and down 5

Given the parent function $$f\left(x\right)=\sqrt[]{x}$$ , check all that apply if f(x) is transformed to -1/2f(x-4)+5

The function f(x) has been vertically compressed by a factor of 1/2

The function f(x) has been reflected about the x-axis

The function f(x) has been vertically stretched by a factor of 1/2

The function f(x) has been reflected about the y- axis

Given the parent function $$f\left(x\right)=\frac{1}{x}$$ , check all that apply if f(x) is transformed to -f(x-4)+5

The transformed function can be written $$-\frac{1}{x-4}+5$$

The Transformed function will have a discontinuity/vertical asymptote at x = 4

The transformed function can be written $$-\frac{1}{x+4}-5$$

The transformed function has been translated right 4 and down 5

Given the parent function $$f\left(x\right)=\frac{1}{x}$$ , check all that apply if f(x) is transformed to -f(x-4)+5

The transformed function f(x) has been reflected about the x-axis.

The transformed function is increasing on the interval $$\left(-\infty,\infty\right)$$ except for x=4

The transformed function is decreasing on the interval $$\left(-\infty,\infty\right)$$ except for x=4

The transformed function has end behavior in which the graph is approaching y=4 or $$x\rightarrow\infty,\ \ y\rightarrow4$$

Outcome 2 Transformations and Interval Notation

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Mathematics

10th - 12th Grade

Used 5+ times

Outcome 2 Transformations and Interval Notation

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26 questions

Show all answers

MULTIPLE SELECT QUESTION

45 sec • 1 pt

Match the statements mean the same as the graph shown.

x ≤ 3

x < 3

MULTIPLE SELECT QUESTION

45 sec • 1 pt

Match the statements mean the same as the graph shown.

x > -2

x ≥ -2

MULTIPLE SELECT QUESTION

45 sec • 1 pt

Match the statements mean the same as the graph shown.

-3 < x < 4

(-3,4]

-3 < x ≤ 4

[-3,4)

MULTIPLE SELECT QUESTION

45 sec • 1 pt

Pick the matching inequality and interval statement?

x > 2 and x ≤ -3

x > 2 or x ≤ -3

MULTIPLE SELECT QUESTION

45 sec • 1 pt

Which statements are true

Graph two can be modeled with the interval

[-2,3]

MULTIPLE SELECT QUESTION

45 sec • 1 pt

MULTIPLE SELECT QUESTION

45 sec • 1 pt

Given the function h(x)= 6.4 and g(x)=8+2x check all that apply regarding h(x)>g(x).

The firsts step is solving the statement h(x)>g(x) algebraically is to divide by 2

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