微積分
極限、導數、最優化與函數性質。
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16. what are the x and y intercepts of the graph? a. (3,0)and (0,3) b. …
b. \((-3,0)\) and \((0,3)\) ### Question 17
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8. find all the zeros of the function f(x) = 2x⁴ + x³ + x² + x − 1
The zeros of the function \(f(x) = 2x^4 + x^3 + x^2 + x - 1\) are \(x = \frac{1}{2}\), \(x = -1\), \(x = i\), and \(x = -i\).
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evaluate the factorial expression. \\(\\frac{20!}{17!}\\) \\(\\frac{20!…
\(6840\)
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a hockey puck slid across an ice rink in 6 seconds. it slid from the ce…
27
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743 + (-242) = -28 + 453 =
For \(743+(-242)\), the answer is \(501\); for \(-28 + 453\), the answer is \(425\)
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an ostrich is being hunted by a lion. the ostrich is running west twice…
84
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the function ( y = f(x) ) is graphed below. what is the average rate of…
14
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write $15\\frac{4}{5}$ as a decimal. $15\\frac{4}{5}=\\square$
15.8
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write $6\\frac{1}{2}$ as a decimal. $6\\frac{1}{2}=\\square$
\( 6.5 \)
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write \\(\\frac{77}{20}\\) as a decimal.
3.85
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write \\(\frac{7}{25}\\) as a decimal.
\(0.28\)
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an ostrich is being hunted by a lion. the ostrich is running west twice…
13
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question 8 consider the following polynomial. q(x) = -3x² - 6x + 14 ste…
As \( x\to-\infty \), \( q(x)\to\boxed{-\infty} \); as \( x\to\infty \), \( q(x)\to\boxed{-\infty} \)
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find the exact value of cos(-π). cos(-π) =
-1
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danny has been bowling for 600 seconds. his bowling ball is currently r…
4.5
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use the aleks calculator to evaluate each expression. round your answer…
For \(275e^{-0.65}\), the answer is \(143.563\); for \(e^{0.1}\), the answer is \(1.105\).
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use the aleks calculator to evaluate each expression. round your answer…
\( e^{-0.2}\approx\boxed{0.819} \) \( 230e^{0.35}\approx\boxed{326.386} \)
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question 1 4 pts what is the average rate of change where x ∈ 0, 1? wha…
For \( x \in [0, 1] \): \( \frac{1}{2} \) (assuming the function is \( y = 2^x - 1 \), at \( x = 0 \), \( y = 0 \); at \( x = 1 \), \( y = 1 \), so average rate is \( \frac{1 - 0}…
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what is the average rate of change where x ∈ 0, 1? what is the average …
For \( x \in [0, 1] \): \( 2 \) For \( x \in [-1, 1] \): \( 1.5 \) Equation of asymptote: \( y = 0 \)
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write the equation of the asymptote. do not use any spaces in your equa…
y=-2
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state the domain and range using interval notation. x ∈ ( select , sele…
Domain: $x\in(-\infty, \infty)$; Range: $y\in(-4, \infty)$ (Note: The actual values may vary slightly depending on the exact graph, but the process is to identify the domain as al…
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what role did income tax primarily play in the u.s. economy following w…
It provided the U.S. the ability to pay off incurred war debts.
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find a formula for the inverse of the following function, if possible. …
\( G^{-1}(x)=\frac{x^{3}-2}{4} \)
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watch out for that intersection practice problems(online) use the desmo…
The two equations are \( y=-x - 8 \) (Equation I) and \( y=\frac{2}{3}x + 2 \) (Equation II)
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lesson 12 refine 2 michael rides his bike $2\\frac{2}{3}$ miles on satu…
\(4\frac{1}{2}\) miles (or \(\frac{9}{2}\) miles)
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in the early u.s., voting among white men was largely limited along wha…
A. property ownership
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23×43 55×26 = use distributive property of multiplication to find. 3×64…
\( 3\times645 = 1935 \)
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apply it 1 what is \\(\\frac{3}{5} + \\frac{13}{15}\\)? show your wo
$\frac{22}{15}$ (or $1\frac{7}{15}$)
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find the inverse of the one-to-one function. f(x) = (x - 4)^3 f^{-1}(x)…
\( \sqrt[3]{x}+4 \)
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graph the line. $y = -dfrac{3}{4}x - 1$
# Explanation: ## Step1: Identify the slope and y-intercept The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For …
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practice & problem solving classify each function as even, odd, or neit…
Even ### Problem 37:
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functions and lines table for a linear equation fill in the table using…
When \( x = -2 \), \( y = 9 \); when \( x = -1 \), \( y = 7 \); when \( x = 0 \), \( y = 5 \); when \( x = 1 \), \( y = 3 \)
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6 4 × 60 = ? basic fact: ______ × ______ = ______ 4 × 60 = ______ 8 6 ×…
- Problem 6: Basic fact: \(4\times6 = 24\) \(4\times60=\boldsymbol{240}\) - Problem 8: Basic fact: \(6\times3 = 18\) \(6\times300=\boldsymbol{1800}\) - Problem 10: Basic fact: \(8…
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9. which expression has a product of 180? a. 3 × 80 b. 60 × 4 c. 3 × 60…
C. \(3\times60\)
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which number makes the equation true $4 \\times 30 = c$ a. 120 b. 124 c…
For \(4 \times 30 = c\): A. 120 For \(8 \times 6 =?\): B. 48
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d. 6×6=36 4. which shows a correct method for finding 7×12? a. 7×10 + 7…
A. \(7\times 10 + 7\times 2\)
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graph the function. plot at least three points. k(x) = 9^x part: 0 / 2 …
For \( x=-1 \), \( k(x)=\frac{1}{9} \); for \( x = 0 \), \( k(x)=1 \); for \( x = 1 \), \( k(x)=9 \) So the completed table (from top to bottom in the \( k(x) \) column) is \(\fra…
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2. which of these makes the equation tr ______ = 7×4 a. 28 b. 30 c. 32 …
A. 28
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trey jogs (\frac{1}{4}) miles from his house. he then jogs (2\frac{3}{8…
$3\frac{5}{8}$
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5. a caterer charges a setup fee and a flat amount per person served. i…
\( y = 13x+69 \) ### Part (b)
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question complete the standard multiplication algorithm for 96 × 0.79, …
The first box (above 96) is 8, and the two boxes below are 64. So: 8 96 x0.79 ------ 64 (Note: This is the first partial product from multiplying 96 by 9. The next step would be m…
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write an equation of the inverse for the one - to - one function as def…
\( a^{-1}(x)=\frac{-x + 9}{2} \) (or \( a^{-1}(x)=-\frac{1}{2}x+\frac{9}{2} \))
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4. 39 + 1 - 24 / 6 = 6. 10 + 28 ÷ 14 - 5 =
For problem 4: \(36\) For problem 6: \(7\)
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8. 5 + 3² * 4 / 2 = ______
23
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choose yes or no to tell if the fraction \\(\\frac{1}{2}\\) will make e…
Yes
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find $f^{-1}(x)$ given that $f(x) = 8^x$. $f^{-1}(x) = $
\(\log_{8}x\) (or \(\frac{\ln x}{\ln 8}\) or \(\frac{\log x}{\log 8}\))
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a line passes through the point (9, 4) and has a slope of \\(\\frac{4}{…
$y - 4=\frac{4}{3}(x - 9)$
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use the graph below to find the average rate of change of the function …
\(-1\)
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refer to the functions defined below. $f(x)=x + 3$\t$h(x)=x^2 + 6$ find…
None
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divide the complex number. write the answer in the form a + bi. express…
\(\frac{44}{65}+\frac{12}{65}i\)
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solve the equation \\(dfrac{ln(x + 2)}{ln(2x - 3)} = 1\\). if no soluti…
\(x = 5\)
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question simplify the expression below using order of operations. (-7)^…
\(-5.4\)
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question simplify the expression below using order of operations. 3 + (…
13
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question simplify the expression below using order of operations. -6.3 …
$\approx -5.83$ (o el valor más preciso según el cálculo detallado: $-6.3 + \frac{4.2}{8.9} = -6.3 + \frac{42}{89} = \frac{-6.3\times89 + 42}{89} = \frac{-560.7 + 42}{89} = \frac{…
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question simplify the expression below using order of operations. -1.4 …
\(2.1\)
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find $f(x)$ given that $f^{-1}(x) = \\log_{9}(x)$. $f(x) = $
\( 9^{x} \)
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the graph of $f(x) = \\log_{2}(2x)$ is shown below. use the graph to ex…
$f(x) = 1 + \log_2(x)$
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the function $f(x) = \\frac{1}{x^2 - 9}$ is a rational function. answer…
A. The horizontal asymptote is \( y = 0 \)
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the function $f(x) = \\frac{1}{x^2 - 9}$ is a rational function. answer…
B. The function has two vertical asymptotes. The leftmost asymptote is \( x=-3 \) and the rightmost asymptote is \( x = 3 \).
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homework: practice what you missed final exam part b question part 5 of…
B. The function has no x - intercept.
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the function $f(x) = \\frac{1}{x^2 - 9}$ is a rational function. answer…
A. The y-intercept is \( y = -\frac{1}{9} \)
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answer the questions below about the following function: $f(x) = -4 \\l…
The domain of \( f(x) \) is \( (0, \infty) \) (or all real numbers \( x \) where \( x > 0 \)) ### Part (b)
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answer the questions below about the following function: $f(x) = \\log_…
The domain of \( f(x) \) is \( (0, \infty) \) (or \( x>0 \)) ### Part (b)
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use the given logarithmic function to answer the following questions. $…
Domain: \( (1, \infty) \) Range: \( (-\infty, \infty) \) ### Part (b)
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d) shift + mouse wheel to zoom shift + mouse drag to pan ( \boldsymbol{…
\( f(x)=-\log_2(x + 5) \) (the first option)
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c) o $f(x) = -5 + \\log_{2} x$ o $f(x) = \\log_{2} (x - 4)$ o $f(x) = -…
\( \boldsymbol{f(x) = \log_2 (x - 4)} \) (corresponding to the option " \( f(x) = \log_2 (x - 4) \) ")
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Question was provided via image upload.
\( f(x)=3+\log_2 x \) (the first option: \( \boldsymbol{f(x)=3 + \log_2 x} \))
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a) graph of a logarithmic function on a coordinate plane with x-axis an…
\(f(x)=-5+\log_2x\) (the option: \(\boldsymbol{f(x)=-5+\log_2x}\))
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suppose $f(x) = 17 \\cdot 1.2^x + 65$. a) what is the domain of $f(x)$?…
### Part (a) # Explanation: ## Step1: Analyze the function type The function \( f(x) = 17\cdot1.2^{x}+65 \) is an exponential function. For exponential functions of the form \( a\…
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flappers and the new woman quick check what does the term new woman mea…
C. a woman who resists limitations of society
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match each graph below with the appropriate function. a) options: ( f(x…
\( f(x)=2^{2 - x} \)
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d) options: $f(x) = -2^{x - 2}$ $f(x) = -2^{x}$ $f(x) = 2^{x - 2}$ $f(x…
\(f(x)=2^{x - 2}\) (the option with \(f(x)=2^{x-2}\))
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Question was provided via image upload.
\( f(x)=2^{x} \) (the last option: \( f(x)=2^{x} \))
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b) options: - $f(x) = -2^{x - 2}$ - $f(x) = -2^x$ - $f(x) = 2^{x - 2}$ …
\(f(x)=-2^{x - 2}\) (the first option: \(f(x)=-2^{x - 2}\))
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match each graph below with the appropriate function. a) options: ( f(x…
\( f(x)=-2^{x} \)
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the function $g(x)$ is a transformation of the parent function $f(x) = …
For the transformation: \( f(x) \) was translated down 3 units. For the function \( g(x) \): \( g(x)=x^2 - 3 \)
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use the graph below to find the average rate of change of the function …
\(-\frac{1}{3}\)
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lena bought 2 cds that were each the same price. including sales tax, s…
\$16.30
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multiplying positive google classroom $-dfrac{3}{2} \\times dfrac{3}{4}…
\( -\frac{9}{8} \)
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which equation is a function that is discrete, and has an absolute maxi…
\( y=-x^{2}+8 \), where \( x \) is an integer
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$\\frac{9}{2} \\times \\frac{1}{4}$
\(\frac{9}{8}\)
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question solve the following system of inequalities graphically on the …
A point in the solution set is \( (4,2) \) (other valid points like \( (3,2) \) also exist)
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joe deposits $7000 into an account that pays simple interest at a rate …
$1050$
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ivanna deposits $800 into an account that pays simple interest at a rat…
$32$
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ivanna deposits $800 into an account that pays simple interest at a rat…
$320$
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choose the function types that are both increasing and decreasing for t…
Quadratic functions, Linear absolute value functions
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the graph of a system of a linear equation and a nonlinear equation is …
C. (4, 5)
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match the addition and subtraction problems to their solutions: 1/24, 2…
- $\frac{5}{7} - \frac{3}{7}$ matches $\frac{2}{7}$ - $\frac{1}{6} + \frac{3}{6}$ matches $\frac{2}{3}$ - $\frac{1}{2} + \frac{1}{4}$ matches $\frac{3}{4}$ - $\frac{1}{5} + \frac{…
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practice & problem solving use long division to divide. 24. ( x^4 + 2x^…
The quotient is \( x^3 - 8x + 13 \) and the remainder is \( -25 \), so \( \frac{x^4 + 2x^3 - 8x^2 - 3x + 1}{x + 2} = x^3 - 8x + 13 - \frac{25}{x + 2} \) ### Problem 25: Synthetic …
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solve the following system of inequalities graphically on the set of ax…
Point: \((0,0)\)
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7.3.ip-5 find the sum. use fraction strips to help. \\(\\frac{1}{12} + …
C. $\frac{1}{12}+\frac{1}{6}+\frac{1}{12}=\frac{1}{12}+\frac{2}{12}+\frac{1}{12}=\frac{4}{12}=\frac{1}{3}$ (filling the boxes: 1, 2, 1, 4, 1)
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graph the function. $y = x^2 + 6x + 5$
To graph \( y=x^{2}+6x + 5 \): 1. **Vertex**: \((-3,-4)\) (from vertex form \( y=(x + 3)^2-4 \)). 2. **x - intercepts**: \((-5,0)\) and \((-1,0)\) (from factoring \( (x + 1)(x + 5…
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what is the slope intercept equation
\( y = c \) (where \( c \) is the y - coordinate of the horizontal line)
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sketch a graph by completing the table and plotting the points. \\( g(x…
The table is completed with \( p(x) \) values 0, 2, 4, 6, 8 for \( x = 0,1,4,9,16 \) respectively, and the points \((0,0)\), \((1,2)\), \((4,4)\), \((9,6)\), \((16,8)\) are plotte…
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what is the slope intercept equation
\(y = -\frac{1}{4}x + 1\) (Note: If the points estimated are different, the equation may vary slightly, but the process remains the same. The key is to correctly identify two poin…
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sketch a graph by completing the table and plotting the points. $p(x) =…
For \( x = 0 \), \( p(x)=0 \); for \( x = 1 \), \( p(x)=2 \); for \( x = 4 \), \( p(x)=4 \); for \( x = 9 \), \( p(x)=6 \); for \( x = 16 \), \( p(x)=8 \). So the table values (fr…
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sketch a graph by completing the table and plotting the points. \\( p(x…
For \( x = 0 \), \( p(x)=0 \); for \( x = 1 \), \( p(x)=2 \); for \( x=-4 \), \( p(x) \) is undefined (no real - valued output); for \( x = 9 \), \( p(x)=6 \); for \( x = 16 \), \…
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a dog groomer charges a total price that is dependent on the weight of …
\$100
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g(0) = \\square
\(-2\)
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the graph of a function f is shown below. find f(1).
\(2\)