5272道题目5525 条题源记录 · 相同内容已合并
指数式・指数方程与函数特征挑战
\( y=3\left(\frac{a}{6}\right)^{x+c}-b \)
How many times does the graph of the given equation in the xy-plane cross the x-axis, where a, b, and c are positive constants such that \( a>6 \) and \( b>c \)?
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指数式・指数方程与函数特征挑战
The functions \(f\) and \(g\) are defined by the given equations, where \(x\ge0\), \(a\) and \(b\) are integer constants, \(a<b\), and \(a>1\). If \(y=f(x)\) and \(y=g(x)\) are graphed in the \(xy\)-plane, which of the following equations displays, as a constant or coefficient, the minimum value of the function it defines, where \(x\ge0\)?
I. \(f(x)=a(0.63)^{-bx}\)
II. \(g(x)=a(1.37)^{x+2}+b\)
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指数式・指数方程与函数特征挑战
The table shows three values of x and their corresponding values of y for the equation \( y=7(2)^x+8 \). In the table, a is a constant. What is the value of a?
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指数式・指数方程与函数特征进阶
The table below shows three values of x and their corresponding values of y for the equation \( y=6(2)^x+4 \). In the table, a is a constant. What is the value of a?
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指数式・指数方程与函数特征挑战
The function \( f \) is defined by the equation \( f(x)=20^x+b \), where b is a constant. In the xy-plane, the graph of \( y=f(x) \) contains the points \( (0,\ 36) \) and \( (2,\ p+19) \), where p is a constant. What is the value of p?
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指数式・指数方程与函数特征进阶
What is the y-intercept of the graph of \( y=4^{x+2} \) in the xy-plane?
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指数式・指数方程与函数特征进阶
An exponential function \( f \) is defined by \( f(x)=k(4)^x \), where k is a positive constant. If \( f(-1)=7 \) and \( f(2)=448 \), what is the value of k?
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指数式・指数方程与函数特征基础
For the function h, the table gives three values of x and their corresponding values of \( h(x) \). Which equation could define h?
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指数式・指数方程与函数特征挑战
The function \( f \) is defined by \( f(x)=a^x-b \) , where a and b are constants. In the xy-plane, the graph of \( y=f(x) \) passes through the points (c, 11) and (2c, 221), where c is a constant. Which of the following could be the value of b?
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指数式・指数方程与函数特征挑战
The table shows three values of x and their corresponding values of y for the equation \( y=5(2)^x+9 \) . In the table, a is a constant. What is the value of a?
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指数式・指数方程与函数特征进阶
The expression \( \frac{6x^{22}}{18x^5} \) is equivalent to \( \frac{1}{3}x^b \), where b is a constant and \( x>0 \). What is the value of b?
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指数式・指数方程与函数特征进阶
The graph of \( y=f(x)+2 \) is shown, where \( f \) is defined by an equation of the form \( f(x)=ab^x+c \). If a, b, and c are integer constants and \( c\le0 \), which equation could define \( f \)?
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