8th Grade Math Flashcards: Compare Functions In Different Representations

What this deck covers

This deck focuses on Compare Functions In Different Representations, giving you a quick way to review the definitions, rules, and examples that matter most for 8th Grade Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Which statement best compares slopes: $m=-2$ versus $m=1$?

Answer: $1$ is greater than $-2$. Positive slopes indicate increasing functions; negative slopes indicate decreasing.

Flashcard 2: What is the slope of a line passing through $(0,3)$ and $(2,7)$?

Answer: $2$. Using slope formula: rac{7-3}{2-0}=rac{4}{2}=2.

Flashcard 3: What property of a linear function equals its rate of change in $y=mx+b$?

Answer: The slope $m$. In $y=mx+b$, the coefficient $m$ represents how much $y$ changes per unit change in $x$.

Flashcard 4: What is the rate of change of the function $y=-3x+7$?

Answer: $-3$. The coefficient of $x$ in $y=mx+b$ form gives the rate of change.

Flashcard 5: What is the initial value (starting value) of the function $y=4x-9$?

Answer: $-9$. The initial value is the $y$-intercept, found when $x=0$: $y=4(0)-9=-9$.

Flashcard 6: Which function has the greater rate of change: $f(x)=2x+1$ or $g(x)=-x+5$?

Answer: $f(x)$. $f(x)$ has slope $2$ while $g(x)$ has slope $-1$, so $f(x)$ changes faster.

Flashcard 7: Which function is increasing: f(x)=- rac{1}{2}x+3 or g(x)= rac{3}{4}x-2?

Answer: $g(x)$. $g(x)$ has positive slope rac{3}{4}, while $f(x)$ has negative slope -rac{1}{2}.

Flashcard 8: Identify the rate of change for a function described as "$y$ decreases $5$ for each increase of $1$ in $x$".

Answer: $-5$. A decrease of $5$ per unit increase means the slope is negative: $-5$.

Flashcard 9: Identify the initial value for a function described as "When $x=0$, $y=12$".

Answer: $12$. The initial value is the $y$-value when $x=0$.

Flashcard 10: Which representation shows a constant rate of change: a straight-line graph or a curved graph?

Answer: A straight-line graph. Linear functions have constant slope, appearing as straight lines on graphs.

Flashcard 11: What formula finds rate of change between points $(x_1,y_1)$ and $(x_2,y_2)$?

Answer: $\frac{y_2-y_1}{x_2-x_1}$. This formula calculates slope as rise over run between two points.

Flashcard 12: Which table shows the greater rate of change: A has $(0,1),(2,5)$; B has $(0,1),(2,3)$?

Answer: Table A. Table A: slope =rac{5-1}{2-0}=2; Table B: slope =rac{3-1}{2-0}=1.

Flashcard 13: What is the slope of a horizontal line (constant function) such as $y=6$?

Answer: $0$. Horizontal lines have no vertical change, so slope equals zero.

Flashcard 14: What is the slope of a vertical line such as $x=2$?

Answer: Undefined. Vertical lines have no horizontal change, making slope division by zero.

Flashcard 15: Which function has the greater initial value: $f(x)=3x-4$ or $g(x)=-2x+1$?

Answer: $g(x)$. $f(0)=-4$ and $g(0)=1$, so $g(x)$ has the greater initial value.

Flashcard 16: Which function decreases faster: $f(x)=-4x+2$ or $g(x)=-x-10$?

Answer: $f(x)$. $f(x)$ has slope $-4$ (more negative) versus $g(x)$ with slope $-1$.

Flashcard 17: Identify the missing value if a linear table has constant rate $3$: $(0,2)$, $(1,5)$, $(2,?)$.

Answer: $8$. With rate $3$, each $x$ increase of $1$ adds $3$ to $y$: $5+3=8$.

Flashcard 18: What is the rate of change from the table points $(1,5)$ and $(3,9)$?

Answer: $2$. Using slope formula: $\frac{9-5}{3-1}=\frac{4}{2}=2$.

Flashcard 19: Which function has greater slope: line through $(0,0)$ and $(4,8)$ or y= rac{3}{2}x+1?

Answer: The line through $(0,0)$ and $(4,8)$. Line has slope rac{8-0}{4-0}=2, greater than rac{3}{2} from the equation.

Flashcard 20: Which is larger: the rate of change $\frac{1}{3}$ or $\frac{2}{5}$?

Answer: $\frac{2}{5}$. Converting to decimals: $\frac{1}{3} \approx 0.33$ and $\frac{2}{5} = 0.4$.

Flashcard 21: What is the slope of a vertical line given by $x=-2$?

Answer: Undefined. Vertical lines have zero run in the slope formula.

Flashcard 22: Identify whether the function is increasing, decreasing, or constant if $m<0$.

Answer: Decreasing. Negative slopes go down from left to right.

Flashcard 23: Identify whether the function is increasing, decreasing, or constant if $m>0$.

Answer: Increasing. Positive slopes go up from left to right.

Flashcard 24: What is the rate of change from the table points $(1,4)$ and $(3,10)$?

Answer: $3$. Use $m=\frac{10-4}{3-1}=\frac{6}{2}=3$.

Flashcard 25: What is the rate of change from the table points $(0,-1)$ and $(2,5)$?

Answer: $3$. Use $m=\frac{5-(-1)}{2-0}=\frac{6}{2}=3$.

Flashcard 26: Which function has the greater rate of change: $f(x)=2x-1$ or table $(0,0)$, $(2,3)$?

Answer: $f(x)=2x-1$. $f$ has slope $2$; table has slope $\frac{3-0}{2-0}=1.5$.

Flashcard 27: Which function has the greater rate of change: $g(x)=-x+6$ or table $(1,2)$, $(4,8)$?

Answer: The table function. $g$ has slope $-1$; table has slope $\frac{8-2}{4-1}=2$.

Flashcard 28: Which function is steeper: $y=\frac{1}{2}x+1$ or $y=-\frac{3}{4}x+2$?

Answer: $y=-\frac{3}{4}x+2$. Compare absolute values: $|\frac{1}{2}|<|\frac{3}{4}|$.

Flashcard 29: Which slope is greater: $m_1=-2$ or $m_2=-\frac{1}{2}$?

Answer: $m_2=-\frac{1}{2}$. $-\frac{1}{2}$ is closer to zero, so it's greater.

Flashcard 30: Which function has the greater initial value: $f(x)=3x-2$ or $g(x)=3x+5$?

Answer: $g(x)=3x+5$. Compare y-intercepts: $-2<5$.