Question
show how you obtained your answers in a step-by-step manner. 1. If f(x) = 4x2 - 3x + 2, find f(-1). 2. State the domain of the function f(x) = (x+3)/(x-1). 3. Write the equation of the line that passes through the points (1, 1) and (2, 4). Write your answer in slope-intercept form. 4. Write the equation of the line with a slope of 2/3 and y-intercept of 1. Write your answer in slope-intercept form. 5. Solve the equation: (4x+1)(2x-7) =0. 6. If f(x) = 4x + 3, evaluate f(x+h). 7. If g(x) = x², evaluate g(x+h). 8. If f(x) = -x + 1, evaluate f(x+h). 9. If f(x) = -x + 1, evaluate f(x-h). 10. Use the quadratic formula to solve the equation: x² - x - 1 = 0
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Answer to a math question show how you obtained your answers in a step-by-step manner. 1. If f(x) = 4x2 - 3x + 2, find f(-1). 2. State the domain of the function f(x) = (x+3)/(x-1). 3. Write the equation of the line that passes through the points (1, 1) and (2, 4). Write your answer in slope-intercept form. 4. Write the equation of the line with a slope of 2/3 and y-intercept of 1. Write your answer in slope-intercept form. 5. Solve the equation: (4x+1)(2x-7) =0. 6. If f(x) = 4x + 3, evaluate f(x+h). 7. If g(x) = x², evaluate g(x+h). 8. If f(x) = -x + 1, evaluate f(x+h). 9. If f(x) = -x + 1, evaluate f(x-h). 10. Use the quadratic formula to solve the equation: x² - x - 1 = 0
Murray
4.590 Answers
1. f(x) = 4x^2 - 3x + 2
f(-1) = 4(-1)^2 - 3(-1) + 2
= 4(1) + 3 + 2
= 4 + 3 + 2
= 9
\text{Answer: } 9
2. The domain is all real numbers except where the denominator is zero.
x - 1 \neq 0
x \neq 1
\text{Domain: } (-\infty, 1) \cup (1, +\infty)
3. Calculate the slope:
m = \frac{4 - 1}{2 - 1} = \frac{3}{1} = 3
Use point-slope form:
y - 1 = 3(x - 1)
Solve for y:
y - 1 = 3x - 3
y = 3x - 2
\text{Answer: } y = 3x - 2
4. Use slope-intercept form \(y = mx + b\):
y = \frac{2}{3}x + 1
\text{Answer: } y = \frac{2}{3}x + 1
5. Set each factor equal to zero:
4x + 1 = 0 \quad \text{or} \quad 2x - 7 = 0
Solve each equation:
4x = -1 \quad \text{or} \quad 2x = 7
x = -\frac{1}{4} \quad \text{or} \quad x = \frac{7}{2}
\text{Answer: } x = -\frac{1}{4}, \ x = \frac{7}{2}
6.f(x) = 4x + 3
f(x+h) = 4(x+h) + 3
= 4x + 4h + 3
\text{Answer: } 4x + 4h + 3
7.g(x) = x^2
g(x+h) = (x+h)^2
= x^2 + 2xh + h^2
\text{Answer: } x^2 + 2xh + h^2
8.f(x) = -x + 1
f(x+h) = -(x+h) + 1
= -x - h + 1
\text{Answer: } -x - h + 1
9.f(x) = -x + 1
f(x-h) = -(x-h) + 1
= -x + h + 1
\text{Answer: } -x + h + 1
10. Solve using the quadratic formula:
ax^2 + bx + c = 0
a = 1, b = -1, c = -1
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
x = \frac{1 \pm \sqrt{1^2 - 4(1)(-1)}}{2(1)}
x = \frac{1 \pm \sqrt{1 + 4}}{2}
x = \frac{1 \pm \sqrt{5}}{2}
\text{Answer: } x = \frac{1 \pm \sqrt{5}}{2}
2. The domain is all real numbers except where the denominator is zero.
3. Calculate the slope:
Use point-slope form:
Solve for y:
4. Use slope-intercept form \(y = mx + b\):
5. Set each factor equal to zero:
Solve each equation:
6.
7.
8.
9.
10. Solve using the quadratic formula:
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